2 ArcSin[Sqrt[

1 - (R - Sqrt[-1 + R^2])^2 Tan[

1/2 (-m + \[Pi])]^2]/(\[Sqrt](1 + (-(R - Sqrt[-1 + R^2]) Sec[

1/2 (-m + \[Pi])] +

R Csc[1/2 (-m + \[Pi])] Sin[m])^2 - (R -

Sqrt[-1 + R^2])^2 Tan[1/2 (-m + \[Pi])]^2))]

2 \sin ^{-1}\left(\frac{\sqrt{1-\left(R-\sqrt{R^2-1}\right)^2 \tan ^2\left(\frac{\pi -m}{2}\right)}}{\sqrt{-\left(R-\sqrt{R^2-1}\right)^2 \tan ^2\left(\frac{\pi -m}{2}\right)+\left(R \sin (m) \csc \left(\frac{\pi -m}{2}\right)-\left(R-\sqrt{R^2-1}\right) \sec \left(\frac{\pi -m}{2}\right)\right)^2+1}}\right)

2ArcSin[Sqrt[1-(R-Sqrt[-1+R^2])^2 Tan[1/2 (-m+\[Pi])]^2]/(\[Sqrt](1+(-(R-Sqrt[-1+R^2]) Sec[1/2 (-m+\[Pi])]+R Csc[1/2 (-m+\[Pi])] Sin[m])^2-(R-Sqrt[-1+R^2])^2 Tan[1/2 (-m+\[Pi])]^2))]