Killing wasn't a Jedi way, no matter how much big the threat is. Sidious was unarmed and weak, too. Windu could have arrested Sidious easily. But, still he didn't care. He even ignored Anakin's words. Why? He said that a Sith was too dangerous to be kept alive. But, still killing wasn't a Jedi way and proper way of doing this was to discuss this with Jedi council first.
Assuming Windu was a Jedi without darkness, why did he choose this way?