sin(x+π/3)+2sin(x-π/3)-√3*cos(2π/3-x)
=sinx*1/2+cosx*√3/2+2sinx*1/2-2cosx*√3/2-√3*(-1/2)cosx-√3*√3/2*sinx
=(1/2+1-3/2)sinx+(√3/2-√3+√3/2)cosx
=0