I am currently studying Complex analysis from the book "Visual Complex Analysis" by Tristan Needham. In the chapter "Non-Euclidian Geometry" on page 282 the author says that the compostions of two Rotations is a Rotation and since a Rotation on a sphere can be decomposed into two reflections. $$R_q^\phi\bullet R_q^\theta = (\mathcal{R_N\bullet R_M})\bullet (\mathcal{R_M \bullet R_L}) = \mathcal{R_N \bullet R_L} = \mathcal{R_r^\psi}$$
Then the author says that the angle $\psi$ can be found out by looking at the white spherical triangle. The area of the Triangle is $A$ and curvature of sphere is $k$ so the sum of the angles
$\theta/2 + \phi/2 + (\pi-\psi/2)= \pi + kA $ so $\psi = \theta+\phi-2kA$. But this is not the formula that is written on the book. Where am i wrong?
