Pi and Pythagorean triples

Geometry Level 4

\[ \large \frac1{8\pi} \left( \sin^{-1} \left(\frac35\right) + \sin^{-1} \left(\frac{12}{13}\right) + \sin^{-1} \left(\frac{63}{65} \right) \right) = \ ? \]

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