# 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.

###### Try it's sister problem: Why do I insert 2015 anywhere I like? #1
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