My question is: Given that the angles $\alpha , \beta,\gamma$ are connected by relation $$2 \tan^2 \alpha\cdot\tan^2 \beta\cdot\tan^2 \gamma + \tan^2 \alpha\cdot \tan^2 \beta +\tan^2 \beta\cdot \tan^2 \gamma+\tan^2 \gamma\cdot\tan^2 \alpha =1 $$ Find the value of $$\sin^2 \alpha+\sin^2 \beta+\sin^2 \gamma$$
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