Problem

Problem

Let x∈(0,π2)x \in \left(0, \frac{\pi}{2}\right) and log⁡24sin⁡x(24cos⁡x)=32\log_{24 \sin x} (24 \cos x) = \frac{3}{2} , then find the value of csc⁡2x\csc^2 x .

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