= Solution
The angular interval has width $\pi$, so its <continuous uniform distribution> has <probability density function>
$$
\boxed{g(\theta)=\begin{cases}1/\pi,&-\pi/2<\theta<\pi/2,\\0,&\text{otherwise}.
\end{cases}}
$$
Integrating this <probability density function> gives the <cumulative distribution function>
$$
\boxed{G(\theta)=\begin{cases}0,&\theta\le-\pi/2,\\\frac12+\theta/\pi,&-\pi/2<\theta<\pi/2,\\1,&\theta\ge\pi/2.\end{cases}}
$$
Values of the <probability density function> at the two individual endpoints may be assigned arbitrarily without changing any <probability>.
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