Your IE comes too late, with too little critical chance to really capitalize on the passive. Plus you're also lacking in attack speed; you look like an AD caster, not an AD Carry. Considering that you have two Sheens in the description, I'm a bit leery of it.
Also, are you aware that you only have four items in your build? >_>
Doran's are meant to be sold for stronger items later in the game after their purpose is served, depending on how well you're doing and whether or not you need the gold right then.
Instead of Trinity Force, consider the newer Iceborn Gauntlet. It procs the slow on your Q, so it's very, very good for kiting people, which is one of Ezreal's strengths. Plus it's a thousand gold cheaper to fill both your Sheen and your defensive item requirement. Also, I'd recommend one of the PD knockoffs; Statikk Shiv or the actual Phantom Dancer for the movement speed, crit, and AS, and a faster Infinity Edge. Guardian Angel is also a staple of any ADC build at the very end of the game.
I'd end up with Boots->Doran's->Zerker's->Sheen->Infinity Edge rush->Glacial Shroud->Zeal->Iceborn, Statikk Shiv, Guardian Angel, and probably Black Cleaver, Bloodthirster, or Last Whisper, depending on the game.