sin^4theta-sin^3theta*cos^2thetasin4θ−sin3θ⋅cos2θ
=sin^3theta(sintheta-cos^2theta)=sin3θ(sinθ−cos2θ)
now
sin3theta =3sintheta -4sin^3theta=>sin^3theta=3/4sintheta-1/4sin3thetasin3θ=3sinθ−4sin3θ⇒sin3θ=34sinθ−14sin3θ
and cos^2theta=1/2(1+cos2theta)cos2θ=12(1+cos2θ)
Putting these in the main expression it becomes
=sin^3theta(sintheta-cos^2theta)=sin3θ(sinθ−cos2θ)
=(3/4sintheta-1/4sin3theta)(sintheta-1/2(1+cos2theta))=(34sinθ−14sin3θ)(sinθ−12(1+cos2θ))
=(3/4sin^2theta-1/4sin3thetasintheta-3/8sintheta-3/8sinthetacos2theta+1/8sin3theta-1/4sin3theta cos2theta)=(34sin2θ−14sin3θsinθ−38sinθ−38sinθcos2θ+18sin3θ−14sin3θcos2θ)
=(3/8(1-cos2theta)-1/4sin3thetasintheta-3/8sintheta-3/8sinthetacos2theta+1/8sin3theta-1/4sin3theta cos2theta)=(38(1−cos2θ)−14sin3θsinθ−38sinθ−38sinθcos2θ+18sin3θ−14sin3θcos2θ)
=(3/8(1-cos2theta)-1/8(cos2theta-cos4theta)-3/8sintheta-3/16(sin3theta-sintheta)+1/8sin3theta-1/8(sin5theta-sintheta))=(38(1−cos2θ)−18(cos2θ−cos4θ)−38sinθ−316(sin3θ−sinθ)+18sin3θ−18(sin5θ−sinθ))
Pl proceed for simlification