Tan-ning the Sine

Geometry Level 3

tan2α.tan2β+tan2α.tan2γ+tan2β.tan2γ+2tan2α.tan2β.tan2γ=1\begin{aligned} &&\tan^{2}\alpha.\tan^{2}\beta + \tan^{2}\alpha.\tan^{2}\gamma \\ && + \tan^{2}\beta.\tan^{2}\gamma + 2\tan^{2}\alpha.\tan^{2}\beta.\tan^{2}\gamma = 1\end{aligned}

If α,β,γ\alpha, \beta,\gamma satisfy the equation above, find the value of sin2α+sin2β+sin2γ\sin^{2}\alpha + \sin^{2}\beta + \sin^{2}\gamma.

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