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Express (1+tan(1∘))(1+tan(2∘))...(1+tan(45∘))(1+\tan(1^{\circ}))(1+\tan(2^{\circ}))...(1+\tan(45^{\circ}))(1+tan(1∘))(1+tan(2∘))...(1+tan(45∘)) in the form of 2n2^{n}2n and enter the value of nnn.
This problem is part of the set Trigonometry.
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