= Solution
The <tangent function> is strictly increasing on the angular interval. Thus $Y\le y$ is equivalent, up to the zero-probability endpoints, to $\Theta\le\arctan(y/x_0)$. Substituting into the angular <cumulative distribution function> gives
$$
\boxed{F(y)=\frac12+\frac1\pi\arctan\frac y{x_0},\qquad-\infty<y<\infty.}
$$
Its <limits> are zero and one at the two infinite endpoints. This is the construction in which the <tangent of a uniform angle has a Cauchy distribution>.
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