More fun in 2015, Part 18

Algebra Level 5

Let w1,..,w2014w_1,..,w_{2014} be the 2015th roots of unity other than 1. Without resorting to calculus, find k=120141(1+wk)2-\sum_{k=1}^{2014}\frac{1}{(1+w_k)^2}

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