Question

Use trigonometric identities to solve tan(2theta)+tan(theta)=0 exactly for 0

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Answer 1

tan2(∅) ≡ 2tan(∅) / (1 - tan²∅)

Thus,
2tan(∅) / (1 - tan²(∅)) + tan(∅) = 0
2tan(∅) / (1 - tan²(∅)) = -tan(∅)
1 - tan²(∅) = -2
tan²(∅) = 3
∅ = tan⁻¹(√3)
∅ = 4nπ/3