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Product of Cosecants

Source: 2015 AIME I Problem 13

March 20, 2015
AMCAIMEAIME I

Problem Statement

With all angles measured in degrees, the product ∏k=145csc⁡2(2k−1)∘=mn\prod_{k=1}^{45} \csc^2(2k-1)^\circ=m^n, where mm and nn are integers greater than 1. Find m+nm+n.
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