Linear Transformations · Superchallenge problem

Let $W$ be the plane $x + y + z = 0$ in $\mathbb{R}^3$, let $D(x, y, z) = (x, 2y, 3z)$, and let $P$ be the orthogonal projection of $\mathbb{R}^3$ onto $W$. The map $T = P\circ D$ sends $W$ into $W$. Find the determinant of $T$ regarded as a linear map $W\to W$.