# Inspired from AIME problem 6

Geometry Level 5

$s = \prod_{k=1}^{45} \left ( \csc^2(2k-1) + 3 \right )$

Angles measured in degrees.

If $$2s-1 = m^{mn}$$ with positive integers $$m,n$$ and $$m$$ is not a prime, find $$m+n$$.

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