MathCastle
TrigonometrySuperchallengeSum, Difference, and Multiple-Angle Formulas

Sum, Difference, and Multiple-Angle Formulas · Superchallenge problem

The product (3+tan⁡1∘)(3+tan⁡2∘)(3+tan⁡3∘)⋯(3+tan⁡29∘)\left(\sqrt3 + \tan 1^\circ\right)\left(\sqrt3 + \tan 2^\circ\right)\left(\sqrt3 + \tan 3^\circ\right)\cdots\left(\sqrt3 + \tan 29^\circ\right) of 2929 factors equals 2n2^n. Find nn.