Triple Trig Threat!

Geometry Level 2

Given the following:

sin(α+βγ)=12\sin (\alpha + \beta - \gamma) = \frac{1}{2}

cos(β+γα)=12\cos (\beta + \gamma - \alpha) = \frac{1}{2}

tan(α+γβ)=1\tan (\alpha + \gamma - \beta) = 1

Find α+β+γ \alpha + \beta + \gamma in degrees such that all three angles are acute.

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