A geometry problem by Refaat M. Sayed

Geometry Level 4

\[\sin \left( \theta _{1}\right) + \sin \left( \theta _{2}\right) + \sin \left( \theta _{3}\right) =\cos \left( \theta _{1}\right) + \cos \left( \theta _{2}\right) + \cos \left( \theta _{3}\right) = 0 \\ \sin ^{2}\left( \theta _{1}\right) + \sin ^{2}\left( \theta _{2}\right) + \sin ^{2}\left( \theta _{3}\right) = \ ? \]

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