When you cast this spell, draw four cards.
Annihilator 4 (Whenever this creature attacks, defending player sacrifices four permanents.)
When Kozilek, Butcher of Truth is put into a graveyard from anywhere, its owner shuffles their graveyard into their library.
Kozilek’s first ability triggers as you cast it, and that ability resolves before the spell itself. It resolves even if the spell is countered.
Annihilator abilities trigger and resolve during the declare attackers step. The defending player chooses and sacrifices the required number of permanents before they declare blockers. Any creatures sacrificed this way won’t be able to block.
If a creature with annihilator is attacking a planeswalker, and the defending player chooses to sacrifice that planeswalker, the attacking creature continues to attack. It may be blocked. If it isn’t blocked, it simply won’t deal combat damage to anything.