Aganju: okay, here is my attempt: (Actually, the task was 'Black to live', but by killing white, black is living)
Let's first look at below : White cannot play at a because of self atari. After , if white takes at either a or b, black replays or for the double snapback.
unkx80: at ? =)
If instead here, white is helpless after . Any approach move at a, b, or c is self-atari.
Black can play b and then a at leisure; and finally c for the kill.
Now maybe the whole concept would work even better if the sequence is changed? Starting with , and playing / later might kill white for sure? (I leave that for someone else to analyze)
Yes, the throw-in reduces White's liberties in some lines, but Black's in others. So Black should wait to play it until they see which way White plays.