  Let $\omega$ be a point in the upper half plane, and let $\Gamma$ be a
discrete, finite covolume subgroup of $\mathrm{PSL}_2(\mathbb{R})$. We
conjecture an explicit formula for the pair correlation of the angles between
geodesic rays of the lattice $\Gamma\omega$, intersected with increasingly
large balls centered at $\omega$. We prove this conjecture for
$\Gamma=\mathrm{PSL}_2(\mathbb{Z})$ and $\omega$ an elliptic point.
