Trigonometry

Geometry Level 3

\[\large \prod_{k=0}^{45} \left(1 + \tan\left( \dfrac{k\pi}{180} \right) \right) = {2}^{\color{red}{m}}\] \[\large\color{red}{m} = \, ?\]


This question was taken from IME (Instituto Militar de Engenharia - Brazil).
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