# A geometry problem by A Former Brilliant Member

Geometry Level 5

$\begin {cases}\tan \alpha =\dfrac{1}{3} \\ \alpha=6\beta \end {cases}$

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

Answer up to 4 decimal places.

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