Verified answer

the angle measure whose sine is sqrt(3)/2 has a reference angle of 60 degrees,

thus 2x = 60, 120, 420, 480, ...

x = 30, 60, 210, 240, ...

The basic solutions to sina==√ 3/2 are 30 deg and 150 deg and in general,

2x=360n+30 and 2x=360n+150

so x=180n+15 and x=180n+75 where n is any integer.

sin 2x = √3 / 2

2x = 60° , 120° , 420° , 480°

x = 30° , 60° , 210° , 240°