Why do I insert 2015 anywhere I like? #1

Geometry Level 5

sec(2π2015)+sec(4π2015)+sec(6π2015)++sec(2014π2015)= ?\large{\sec \left( \dfrac{2\pi}{2015} \right) + \sec \left( \dfrac{4\pi}{2015} \right) + \sec\left( \dfrac{6\pi}{2015} \right) + \ldots + \sec \left( \dfrac{2014\pi}{2015} \right) = \ ? }


Bonus : Generalize the sum k=1nsec(2kπ2n+1)\displaystyle \sum_{k=1}^n \sec \left( \dfrac{2k\pi}{2n+1} \right) in terms of nn with a proper derivation without using methods like Induction.

Try it's sister problem: Why do I insert 2015 anywhere I like? #2
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