Question

Prove that tan theta+tan 2theta+tan 3theta=tan theta*tan 2theta*tan 3theta

Answer 1

I think you have it wrong:

tan 3θ = tan(θ+2θ)
tan 3θ = (tanθ+tan2θ)/(1-tanθtan2θ)
tan3θ(1-tanθtan2θ) = tanθ+tan2θ
tan3θ - tanθtan2θtan3θ = tanθ+tan2θ
tan3θ - tan2θ - tanθ = tanθtan2θtan3θ