sin^4theta-sin^3theta*cos^2theta
=sin^3theta(sintheta-cos^2theta)
now
sin3theta =3sintheta -4sin^3theta=>sin^3theta=3/4sintheta-1/4sin3theta
and cos^2theta=1/2(1+cos2theta)
Putting these in the main expression it becomes
=sin^3theta(sintheta-cos^2theta)
=(3/4sintheta-1/4sin3theta)(sintheta-1/2(1+cos2theta))
=(3/4sin^2theta-1/4sin3thetasintheta-3/8sintheta-3/8sinthetacos2theta+1/8sin3theta-1/4sin3theta cos2theta)
=(3/8(1-cos2theta)-1/4sin3thetasintheta-3/8sintheta-3/8sinthetacos2theta+1/8sin3theta-1/4sin3theta cos2theta)
=(3/8(1-cos2theta)-1/8(cos2theta-cos4theta)-3/8sintheta-3/16(sin3theta-sintheta)+1/8sin3theta-1/8(sin5theta-sintheta))
Pl proceed for simlification