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TrigonometryChallengeSum, Difference, and Multiple-Angle Formulas

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

Without a calculator, find the exact value of tan⁡20∘+tan⁡25∘+tan⁡20∘tan⁡25∘\tan 20^\circ + \tan 25^\circ + \tan 20^\circ\tan 25^\circ.