# Why do I insert 2015 anywhere I like? #2

**Geometry**Level 5

\[\large{\log_2 \left[\cos \left( \dfrac{2 \pi}{2015} \right) \cos \left( \dfrac{4 \pi}{2015} \right) \cos \left( \dfrac{6 \pi}{2015} \right) \dotsm \cos \left( \dfrac{4028 \pi}{2015} \right) \right]} = \ ?\]

**Bonus** : Generalize \(\displaystyle \prod_{k=0}^{2n} \cos \left( \dfrac{2 k\pi}{2n+1} \right) \) in terms of \(n\) with a proper derivation without using methods like Induction.