Идея такова:
4sin²x-sin x=2sin² x+2cos²x+√3cosx
2sin² x-2cos² x=sin x+√3cos x
-2(cos²x-sin²x)=1/2(√3/2cos+1/2sinx)
cos2x+cos(x-π/6)=0
2cos(3x/2-π/12)cos(x/2+π/12)=0
cos(3x/2-π/12)=0
cos(x/2+π/12)=0
3x/2-π/12=π/2+πn
3x/2=7π/12+πn
x=7π/18+2πn/3
x/2+π/12=π/2+πn
x/2=5π/12+πn
x=5π/6+2πn