Triple Integrals & Coordinate Systems · Superchallenge problem

The solid torus $T$ is $\left(\sqrt{x^2 + y^2} - 2\right)^2 + z^2 \le 1$ and has constant density $1$. Find its moment of inertia about the $z$-axis, $I_z = \displaystyle\iiint_T (x^2 + y^2)\,dV$. Give your answer in terms of $\pi$.