If $15{\sin }^{4}\alpha +10{\cos }^{4}\alpha =6$, for some $\alpha \in R$, then the value of $27{\sec }^{6}\alpha +8{\csc }^{6}\alpha$ is equal to: [JEE Main 2021, 18 Mar (Shift 2)]

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If \(15{\sin }^{4}\alpha +10{\cos }^{4}\alpha =6\), for some \(\alpha \in R\), then the value of \(27{\sec }^{6}\alpha +…

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