Simplifying Sin[3θ] to Simplifying Trigonometric Expressions

[Confusingmeh]

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 don't have the formula i need or what.

 

[rock.freak667]

Sin2θ = 2sinθcosθ, remember that one?