Why do I love 2016 so much?

Geometry Level 5

\[\dfrac{\displaystyle \sum_{n=1}^{2016^2+4032} \sqrt{\sqrt{4034}+\sqrt{2017+\sqrt{n}}}}{\displaystyle \sum_{n=1}^{2016^2+4032} \sqrt{\sqrt{4034}-\sqrt{2017+\sqrt{n}}}}\]

If the value of above expression is in the form \(\cot\dfrac{\pi^a}{b}\), find \(a+b\).

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