How does achilles rage lead to the greeks downfall in the illiad?

Achilles rushes into the temple of Apollo and kills Trollius on the alter, pissing off the god. Later, a weapong guided by Apollo kills Achilles, with either (depending on the story) by a knife stab in the back or an arrow to his heel from Paris. The irony and divine insult being that Paris (or the in) is a coward killing the fearless Achilles.