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Let x,y,zx, y, zx,y,z be the real roots of the cubic equation
2u3−799u2−400u−1=02u^3-799u^2-400u-1=02u3−799u2−400u−1=0
and let ω=tan−1x+tan−1y+tan−1z\omega = \tan^{-1} x+\tan^{-1} y+\tan^{-1} zω=tan−1x+tan−1y+tan−1z. If tanω=ab\tan \omega = \frac{a}{b}tanω=ba, where aaa and bbb are positive coprime integers, what is the value of a+ba+ba+b?
This problem is posed by Russelle G.
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