I found this theorem online and I have no idea how to prove it. I can't find a proof anywhere; if anyone knows one that would be great.
Theorem 6.10
Let $D$ be a hyperbolic triangle with angles $\frac{\pi}{l}, \frac{\pi}{m}$ and $\frac{\pi}{n}$. Then the triangles obtained by inverting (or reflecting) $\triangle$ in each of its sides and then inverting each of the images in each of its sides, and so on indefinitely, cover the hyperbolic plane without gaps or improper overlaps.