Numerical [JEE Main-2021 (March)] Let \( \tan \alpha, \tan \beta \)...

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Numerical
[JEE Main-2021 (March)]
Let \( \tan \alpha, \tan \beta \) and \( \tan \gamma, \alpha, \beta, \gamma \neq \frac{(2 n-1) \pi}{2}, n \in \mathbb{N} \) be
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the slopes of three line segments \( O A, O B \) and \( O C \), respectively, where \( O \) is origin. If circumcentre of \( \triangle A B C \) coincides with origin and its orthocentre lies on \( y \) axis, then the value of \( \left(\frac{\cos 3 \alpha+\cos 3 \beta+\cos 3 \gamma}{\cos \alpha \cos \beta \cos \gamma}\right)^{2} \) is equal to
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