Nebuchadnezzar becomes the narrator, telling a separate incident, also involving a dream, in order to glorify the true God. The king calls Daniel by his Hebrew name, honoring his God. The king sees a prosperous, large tree. But it is cut down and left to the beasts in the wilderness. Daniel says it applies to the king himself, and calls him to repent of his pride. He does not, and the dream comes true: Nebuchadnezzar goes crazy and lives "out in the woods" for 7 years. God restores him, and he is humble, faithfully glorifying Daniel's God.
The next king, Belshazzar, feasts with the temple cups, a great sacrilege. God judges him on the spot - the handwriting is on the wall, and that same night Darius conquers the empire.
Darius sets up a new administration, with Daniel near the top. Envious underlings trick the king into condemning him to death, by forcing a choice between obeying the king or obeying God. Daniel is put in a den, a stone is sealed over it, an angel comes. No harm was found in him, for he was blameless and trusted God. Those who committed the injustice are punished. Does this sound at all familiar!?
Darius also glorifies Daniel's God. Like Nebuchadnezzar he admits His kingdom is everlasting, just as the vision in chapter 2 said. Now, 2 kings, prophesied in the same vision (2:39,44) have confirmed it.