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PrecalculusSuperchallengeAnalytic Trigonometry

Analytic Trigonometry · Superchallenge problem

Find the exact value of tan⁡20∘tan⁡40∘+tan⁡40∘tan⁡60∘+tan⁡60∘tan⁡80∘+tan⁡80∘tan⁡100∘+tan⁡100∘tan⁡120∘+tan⁡120∘tan⁡140∘+tan⁡140∘tan⁡160∘\tan20^\circ\tan40^\circ+\tan40^\circ\tan60^\circ+\tan60^\circ\tan80^\circ+\tan80^\circ\tan100^\circ+\tan100^\circ\tan120^\circ+\tan120^\circ\tan140^\circ+\tan140^\circ\tan160^\circ.