What Formula Connects Cosine To Tangent?

Geometry Level 3

\[ \begin{cases} \cos \alpha = \tan \beta \\ \cos \beta = \tan \gamma \\ \cos \gamma = \tan \alpha \end{cases} \]

The acute angles \(\alpha, \beta\) and \(\gamma\) satisfy the system of equations above. Find \(\sin \gamma\).

Give your answer to 2 decimal places.

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