Question: how does achilles rage lead to the greeks downfall in the illiad? 

Answer: 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 assassin) is a coward killing the fearless Achilles.
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