How was my Ezreal build in this situation?

I bought Doran's Blade -> Tear -> Sheen -> Trinity -> Manamune -> Ionion Boots -> BOTRK -> And then I was going to buy Last Whisper as you can see since I had Giant Slayer in my inventory. However, vs this particular comp and my opponent being Vayne, do you think it's justified to build BOTRK first and then Ionion boots? Or maybe I should have bought Giant Slayer even after my first two items?