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\begin{align*} D = \frac{\arcsin{(X \sin{\theta})} - \theta}{\sin{\theta}} \end{align*} and \begin{align*} X \sim \text{Uniform}[-1, 1], \hspace{0.5in} \theta \sim \text{Uniform}[0, 2 \pi] \end{align*}

How to find the PDF of $D$? or is there anyway to simplify the equation of $D$!?

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    Isn't it that for $\theta<\pi$, $d$ becomes negative?2011-05-04
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    Sorry .. forget about the P(d > 0) .. what about calculating the PDF??2011-05-04

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