If 1cos⁡α⋅cos⁡β+tan⁡α⋅tan⁡β=tan⁡γ\frac{1}{\cos \alpha \cdot \cos \beta} + \tan \alpha \cdot \tan \beta = \tan \gamma ,…

Problem

If 1cos⁡α⋅cos⁡β+tan⁡α⋅tan⁡β=tan⁡γ\frac{1}{\cos \alpha \cdot \cos \beta} + \tan \alpha \cdot \tan \beta = \tan \gamma , where 0<γ<π20 < \gamma < \frac{\pi}{2} and α,β\alpha, \beta are positive acute angles, show that π4<γ<π2\frac{\pi}{4} < \gamma < \frac{\pi}{2}

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