Why do I insert 2015 anywhere I like? #1

Geometry Level 5

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

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

Why do I insert 2015 anywhere I like? #1

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