2016 is coming!

Algebra Level 5

x2016+x2015++x+1 x^{2016} + x^{2015} + \cdots + x + 1

If x1,x2,x3,,x2016x_{1}, x_{2}, x_{3}, \ldots , x_{2016} are the roots of the expression above, find the value of

i=120161(1xi)2.\displaystyle\sum_{i=1}^{2016}\frac{1}{(1 - x_{i})^2}.


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