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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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