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 \(\alpha \beta\).

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