Find all real numbers that satisfy the equation

2sin(2x)+ sqrt3 = 0    subtract square root 3 from both sides

2sin2x  = -√3            divide both sides by 2

sin2x = -√3 / 2

sin x  = -√3 / 2   at 240°  and  at  300°

So sin 2x = -√3 / 2   at  120° and at  150°

More general solutions are  120° + (2pi)n  and 150° + (2pi)n    where n is an integer