  Let $\Gamma< \mathrm{PSL}_2(\mathbb{R})$ be a lattice and $\omega\in
\mathbb{H}$ a point in the upper half plane. We prove the existence and give an
explicit formula for the pair correlation density function for the set of
angles between geodesic rays of the lattice $\Gamma \omega$ intersected with
increasingly large balls centered at $\omega$, thus proving a conjecture of
Boca-Popa-Zaharescu.
