Katara leaves in the winter. The air cools, the palace quiets, and then there is the month when he doesn't sleep. The assassins' darts start getting closer and closer and so Zuko stops sleeping. He dons his black clothing and his blue mask and he slips out into the night and he hunts.
Sometimes it's Azula or his mother that he's chasing and he knows that he is losing his mind but it feels so good to be moving and alive again that Zuko doesn't mind.
He finds them. With help, of course. Mai somehow summoned Ty Lee from wherever she had disappeared to. Together with a few trusted guards they uncover the plot. They chase them down.
Zuko's task is to defang the vipers. He could execute them. He could make an example of them. He could corral and eliminate their entire families, obliterate the conspiracy down to its roots and smallest seeds.
Zuko chooses exile. The Earth Kingdom is more than happy to keep an eye on war-mongering Fire Nation traitors.
It surprises him, how easy it is to let go of vengeance.
All he wants to do is sleep.