How to calculate the PDF or the CDF of $D$ where:
$$D = \sqrt{1 - X^2 \sin^2{\theta}} - X \cos{\theta}$$
If $X$ is uniform distributed on $[-1, 1]$, $\theta$ is uniformly distributed on $[0, 2 \pi]$ and they are independent.
I know that: $$F_D(d) = \iint\limits_D \, f_\theta(\theta) f_X(x) \mathrm{d}x\,\mathrm{d}\theta $$
But I don't know how to find the ranges I should integrate on!