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## Homework Statement

Simplify Sin[3θ] (no double angles)

## Homework Equations

Sin[3θ]=Sin[θ+2θ]

Sin[α + β] = Sin[α] Cos[β] + Cos[α] Sin[β]

Sin[3θ] = 3sinθ - 4sin^3 θ

Cos2θ = 1-2Sin^2θ

## The Attempt at a Solution

Sin[3θ] = sin[θ+2θ]

Sin[θ+2θ] = Sinθ Cos2θ + Cosθ Sin2θ

Sinθ Cos2θ + Cosθ Sin2θ = Sinθ (1-2Sin^2θ) + Cosθ Sin2θ

=Sinθ - 2Sin^3θ + Cosθ Sin2θ This is where i get lost...I know it should end up being

= (3sinθ - 4sin^3 θ) but i cannot figure out how to get there. I don't know whether I just dont have the formula i need or what.