# When I'm gone

Geometry Level 4

Let $$0^{\circ}\leq\alpha,\beta,\gamma\leq90^{\circ}$$ be angles such that $\sin\alpha-\cos\beta=\tan\gamma$$\sin\beta-\cos\alpha=\cot\gamma$

and $$\gamma_{1},\gamma_{2},\ldots,\gamma_{i}$$ are different possible values of $$\gamma$$.Find

$\displaystyle\sum_{i=1}^{n}\gamma_{i}$

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