Tangential problem

Geometry Level 3

(1+tan1)(1+tan2)(1+tan3)(1+tan45) \large (1+\tan 1^{\circ})(1+\tan 2^{\circ})(1+\tan 3^{\circ}) \cdots (1+\tan 45^{\circ})

If the value of the expression above equal to 2n2^n, find the value of nn.

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