The wiki page https://en.wikipedia.org/wiki/Poincaré_disk_model#cite_note-MSE1333850-3 shows a famous image titled "the (6,4,2) triangular hyperbolic tiling". From another entry, it reads "triangular tiles whose vertices have angles $\pi/2,\pi/4,\pi/6$". I guess one angle corresponds to an arc in the disc.
However, I cannot find the right formula that maps an angle $\theta_1$ to an arc (represented as an equation evolving $x,y$, such as $x^2+y^2=1$) in the Poincare disc. Help! thanks!