# Inspired by an undisclosed old problem

Geometry Level 5

$\large 199 x^5+800 x^4+750 x^3+18 x^2-83 x-12 = 0$

Let $$x_1, x_2,x_3,x_4,x_5$$ be roots of the equation above.

If the value of $$\displaystyle \tan\left( \sum_{m=1}^5 \tan^{-1}(x_m) \right)$$ is equals to $$\frac ab$$ for coprime positive integers $$a$$ and $$b$$, what is the value of $$a - b$$?

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