A geometry problem by Abhay Kumar

Geometry Level 5

{tanα=13α=6β \begin {cases}\tan \alpha =\dfrac{1}{3} \\ \alpha=6\beta \end {cases}

Given the above, find 12(csc2β3sec2β)\dfrac{1}{2}\left(\csc 2\beta-3\sec 2\beta\right), if α\alpha is acute angle.

Answer up to 4 decimal places.

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