Why did the writers of the Septuagint (LXX) choose the particular word for wrath and use the optative mood for that word (ὀργιζέσθωσαν) normally translated "angry/rage/wrath" in Psalm 99:1 - "The LORD has assumed kingship, let the peoples be angry." It doesn't at all make sense within the context of the Psalm.
This is one of those problems with people who think the LXX is the English translation of the Greek rather than the Greek itself. E.g. each time you translate, you are replacing one word with a semantic range of its own and picking a different semantic range that overlaps the range of the word.
When you translate again, you do the same thing. So something that is two translations removed (an english translation of a greek translation of Hebrew) is always going to be less accurate than something that is just a single translation removed (an English translation of Hebrew). This does not mean that an English translation from Hebrew is better than a Greek translation from Hebrew. It merely means that for English readers, a translation from Hebrew to Greek to English will be less faithful than a translation from Hebrew to English, just as to Greek readers, a translation from Hebrew to English to Greek will be less faithful than the LXX which is directly from Hebrew to Greek. So Greek readers who could read the Old Greek (which is different from modern Greek) would complain about the same types of things if someone made an Old Greek translation of the ESV, for example, and they would wonder what those ESV translators were thinking about getting the translation so wrong.
Specifically in this case, the greek word orgizo has a semantic range including the following, as per the Lexham Analytical Lexicon of the Septuagint:
חרה 1—be or become hot, angry; get excited; kindle (26): Ge 31:36; Ex 22:24; 32:19, 22; Nu 22:22; 25:3; 32:10, 13; Dt 6:15; 7:4; 29:27; 31:17; Jdg 2:14, 20; 3:8; 6:39; 9:30; 10:7; 14:19; 4 Kgdms 13:3; Job 32:2, 3; Ps 17:8; 105:40; 123:3; Hab 3:8 קצף
1—be angry, be furious; rouse to anger, incense (10): Gen 40:2; 41:10; Nu 31:14; Ec 5:5; Is 57:16; 64:5, 9; Lam 5:22; Zech 1:2, 15
אַף 2—nose; face; anger; (dual) nostrils (7): Ex 22:24; 32:22; Nu 22:22; 25:3; Dt 6:15; Job 32:2,
3 רגז—tremble, quake with fear; get excited (6): Ge 45:24; Ex 15:14; 4 Kgdms 19:28; Ps 4:5; 98:1; Pr 29:9
4 אנף—be angry (said of God) with (6): 3 Kgdms 11:9; Ps 2:12; 59:3; 78:5; 84:6; Isa 12:1 כעס—be vexed; irritate; grieve, disturb; offend, provoke to anger (2): Esd B 14:1; Ps 111:10 עשׁן—be surrounded with smoke; exude smoke (2): Ps 73:1; 79:5
So orgizo is a valid translation choice for the underlying Hebrew, רגז which occurs in 98.1 (99.1 in English translations), but it contains more in its semantic range, and when translated into English the translators chose the English word "angry", which is not what English translators working directly from the Hebrew would choose. That is all that's going on here.
PSALM 99:1 The Lord reigns; let the peoples tremble! [snip]
Greek orgizesthōsan - Let be angry. - Hebrew: rāḡaz - tremble, quake, rage, quiver, be agitated, be excited, be perturbed.
The translation from the Masoretic text, as are all translations, was ‘influenced’, by their established biblical foundation. The authors of the [early] Septuagint would have had a very different ‘foundation’. We know the thinking of that era, (when the Septuagint was ‘penned’) because we have other (non-canonical) writings which help us ‘see’ this.
But let’s look,a little closer - why would this be a factor? Because this Psalm is a prophetic psalm - and we know about how those prophecies were ‘understood’ in the years before Jesus was born, compared to how they were ‘viewed’ later on when the Bibles we use were first translated.
This prophecy is quoted in Revelation .. which provides some more context.
REV 11:18 The nations raged, but your wrath came,
The context is the blowing of the 7th trumpet - the nations had just been reclaimed by Jesus. Revelation (that is, the end times) was well understood by the Hebrews working on the early Septuagint, but ‘arguably’ less well understood by the scholars who penned the traditional doctrines around 15/16th century - and thereby influenced some of the less recent Bible translations.
Wicked people do not want Lord's dominion to encroach upon their habitual dominion of sins and iniquities. λαοί - "pagan people" - here denote those who do not want to live under Lord's commandments, but follow their own ways. So, if the Lord comes to His reign, of course such people will get irritated for that to the point of getting furious.
Of course the λαοί does not mean only non-Jews, but also Jews who cherish their God-less lifestyles and dread the very notion of Lord's reign, for He will definitely abolish such lifestyles. They would rather kill Lord, as they did, than change their mindset and lifestyles. That is why the entire Jerusalem was troubled together with Herod at hearing that Messianic King has been born (Matthew 2:3), because both Herod and the wicked dwellers of Jerusalem whom Herod allowed to live wicked lives were afraid of the righteous King who would abolish iniquity (bribery, brothels, casinos, dogfights etc.). So, they were complacent with Herod ordering killing the 2- year old babes in Bethlehem and the vicinities.
But now this passage should be understood also in a spiritual way: when Lord starts reigning in our hearts and we start to fight sins through Him working in us, demons get furious, for their only desperate joy and hopeless consolation is when they see a man making himself miserable through subjection to sin.
Now, the optative in the Septuagint, "let the nations get angry", means a certain divine "spite", as if the Holy Spirit says: "I am doing everything for them to repent and turn to Me, but they choose their ways, but I cannot help trying to win them to Me, and if this angers them, let them get angry! (NB:divine spite), what can I do, for I cant help loving them". Thus divine "spite" is not spite but unfailing and infinite love.