# So close!

Geometry Level 4

$\prod _{ n=1 }^{ 2016 }{ \sec { \left( \frac { n \pi }{ 2017 } \right) } } ={ \alpha }^{ \beta }$

The equation above holds true for some positive integers $$\alpha$$ and $$\beta$$ with $$\alpha<4$$. Find the sum of the prime factors for $$\alpha \beta$$.

×