Parametric, Polar and Vector-Valued Functions · Superchallenge problem

The spiral $r=\theta$, $\theta\ge0$, winds around the pole infinitely often: it makes its second turn as $\theta$ runs from $2\pi$ to $4\pi$, and its third turn as $\theta$ runs from $4\pi$ to $6\pi$. Find the area of the region that lies between the second and third turns.