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if particular triplets $\alpha_{1},\alpha_{2},\alpha_{3}$ satisfy $\displaystyle -\frac{\pi}{2}<\alpha_{1}<\alpha_{2}<\alpha_{3}<\frac{\pi}{2}$ then number of vaues of

$\displaystyle \theta \in (-\frac{\pi}{2},\frac{\pi}{2})$ satisfy $\displaystyle \prod^{3}_{i=1}(\tan \theta-\tan \alpha_{i})= \displaystyle \sum^{3}_{i=1}(\tan \theta-\tan \alpha_{i})$

i not understand how can i go ahead,some help me, thanks

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    Consider the cubic polygnomial $\prod_{i=1}^3(x-\tan\alpha_i) - \sum_{i=1}^3(x-\tan\alpha_i)$, what is the sign of this polynomial at $\tan\alpha_1$ and $\tan\alpha_3$? – 2017-01-06

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