f(x)=√3 sin2x-2sin²x
= √3 sin2x+1-2sin²x-1
=√3 sin2x+cos2x-1
=2(√3/2 sin2x+1/2cos2x)-1
=2(cos(π/6)sin2x+sin(π/6)cosx)-1
=2sin(2x+π/6)-1