# Sum year we're having

Geometry Level 4

If $$\displaystyle\sum_{k=1}^{2015} \cot^{-1}(2k^{2}) = \cot^{-1}\left( \dfrac{a}{b} \right),$$ where $$a$$ and $$b$$ are positive coprime integers, then find $$a + b.$$

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