# It's not Pythagoras

Geometry Level pending

Let $$a$$, $$b$$, and $$c$$ be the three sides of a triangle, and let $$\alpha$$, $$\beta$$, and $$\gamma$$ be the angles opposite them respectively. If $$a^2+b^2=1989c^2$$, find

$\large \frac{\color{blue}{\tan \alpha \ \tan \beta}}{\color{magenta}{\tan \alpha \ \tan \gamma}+\color{purple}{\tan \beta \ \tan \gamma}}$

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