A geometry problem by Atul Kumar Ashish

Geometry Level 3

(1+tan1)(1+tan2)(1+tan3)(1+tan45)=2n(1+\tan 1^\circ)(1+\tan 2^\circ)(1+\tan 3^\circ) \cdots (1+\tan 45^\circ) = 2^n

The above equation holds true for some positive integer nn. Find nn.

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