cos2(x)+3sin2(x)-1=-2(√3)sin(x)cos(x),
2sin2(x)=-2(√3)sin(x)cos(x),
sin2(x)=-(√3)sin(x)cos(x),
sin(x)=0 is one set of solutions: x=nπ (180n°) where n is an integer. Divide through by sin(x):
sin(x)=-cos(x)√3, tan(x)=-√3, x=2π/3 (120°) or 5π/3 (300°). The set of these solutions is obtained by adding 2πn (360n°) to each of these.
SOLUTION
x=nπ, 2π(3n+1)/3, (6n+5)π/3.