If $ 15 \sin ^{4} \alpha+10 \cos ^{4} \alpha=6 $, for some $ \alpha \in R $, then the value of $ 27 \sec ^{6} \alpha+8 \operatorname{cosec}^{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} \alph…

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