Trigonometry for 2016

Geometry Level 4

\[ \large \sum_{r=1}^N \cos\left( \dfrac{2r \pi}{2N+1} \right) \]

If \(N = 2016\), the value of the summation above is equal to \( -\dfrac AB\), where \(A\) and \(B\) are coprime positive integers, find \(A+B\).

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