Polynomial twister

Algebra Level 4

Let \(x_1,x_2,\ldots,x_{2015} \) be the roots of the equation \[ x^{2015} + x^{2014} + x^{2013} + \ldots + x^2 + x + 1 =0.\] Evaluate

\[ \frac1{1-x_1} + \frac1{1-x_2} + \ldots + \frac1{1-x_{2015}}. \]

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