Linear Transformations · Superchallenge problem

A linear map $T:\mathbb{R}^3\to\mathbb{R}^3$ satisfies $T\circ T = T$ and $\operatorname{tr} T = 2$. Also $T(1,0,0) = (1,0,0)$ and $T(0,1,0) = (1,1,1)$. Find the $x$-coordinate of $T(0,0,1)$.