What Formula Connects Cosine To Tangent?

Geometry Level 3

{cosα=tanβcosβ=tanγcosγ=tanα \begin{cases} \cos \alpha = \tan \beta \\ \cos \beta = \tan \gamma \\ \cos \gamma = \tan \alpha \end{cases}

The acute angles α,β\alpha, \beta and γ\gamma satisfy the system of equations above. Find sinγ\sin \gamma.

Give your answer to 2 decimal places.

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