# Sum of inverse tangents of roots

Geometry Level 4

If $$x_1, x_2, x_3, x_4$$ are rotos to the equation $$x^4 - (\sin2\theta) x^3 + (\cos 2\theta) x^2- x \cos\theta - \sin\theta = 0$$, compute $$\displaystyle \sum_{i=1}^4 \tan^{-1} x_i$$.

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