# Russelle's triple tangent

Algebra Level 4

Let $$x, y, z$$ be the real roots of the cubic equation

$2u^3-799u^2-400u-1=0$

and let $$\omega = \tan^{-1} x+\tan^{-1} y+\tan^{-1} z$$. If $$\tan \omega = \frac{a}{b}$$, where $$a$$ and $$b$$ are positive coprime integers, what is the value of $$a+b$$?

This problem is posed by Russelle G.

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