I will explain the second woe which will take place over a month or two (not 3.5 years)
near the end of the 7 years. The second woe's timing, I show on this chart I made of the seven seals.
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As a result of the trumpet plagues and vials of God wrath poured out during the great tribulation, oil - the life blood of the nations - will become harder to obtain, especially that which is in the middle east.
The beast-king (the Antichrist in his final stage) will be funneling all the middle east oil to the EU and its western nations allies.
Faced with the crisis of dwindling oil, the nations to the north, east, south of Jerusalem will have no choice but to attempt to remove the beast-king and his armies from Jerusalem and the middle east. The kings of the east, China and allies, will make up the 200 million army that will kill a third of mankind as the they march westward (as the second woe takes place).
You are right that Daniel 11:40-41 identifies the actions of the beast-king (the king of the west). My first chart below is based on Daniel 11:40-44. And my second chart below based on Daniel 11:45.
I labeled the first chart as a "prelude to Armageddon" because as the fighting is taking place, unexpectedly the sixth seal event takes place, and the sign of the Son of Man appears place in heaven - Jesus, sickle in hand (see my illustration below).
So all the fighting going on against the beast-king and his armies will stop because the bigger threat.
And that is when the false prophet, the beast king, and Satan (speaking through the statue image of the beast-king) in Revelation 16:13-14 convince the kings of the earth to take up their courage and gather their armies (which will all already be in the middle east) at Armageddon to prepare to make war against Jesus and His armies of heaven.
Jesus will destroys those armies and their kings in Revelation 19:19-21 at His return to this earth.
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