If `2t a n^2alphat a n^2betat a n^2gamma+t a n^2alphat a n^2beta+t a n^2betat a n^2gamma+t a n^2gammat a n^2alpha=1,` prove that `s i n^2alpha+s i n^2beta+s i n^2gamma=1` .

Explanation

To prove that \( \sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma = 1 \) given the equation

\[ 2 \tan^2 \alpha \tan^2 \beta \tan^2 \gamma + \tan^2 \alpha \tan^2 \beta + \tan^2 \beta \tan^2 \gamma + \tan^2 \gamma \tan^2 \alpha = 1, \]

we will follow these steps:

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