Vector Calculus · Challenge problem

The torus $T$ is formed by revolving the circle $(x - 2)^2 + z^2 = 1$ in the $xz$-plane about the $z$-axis. Find the outward flux of $\mathbf F = \left(x - yz^2,\; y + xz^2,\; z\right)$ through the surface of $T$. Give your answer in terms of $\pi$.