I'm confused on how to determine what the end result angles are for a trigonometric identity (I get how to find the value of sin, cos, etc., and I know how to find the reference angle. I just don't know how to determine further angles from there).

Question

For example, 3tan^2x-1 equals the square root of 3 over three. I know 30 degrees is my reference angle. My book says the other answer is 150. But where does this come from? As a general rule, do you find the second angle by subtracting the reference angle from 180 (or 360 if it's that sort of problem)? But this approach doesn't work for the negative sq. root of 2/2=sinx. 360-225 doesn't equal the second angle, 315. So is the way to find the subsequent angles by adding the reference angle (in this case 30) to the degree value of the nearest axis (90, 180, etc)?? Yet this doesn't work for a reference angle of the sq. root +/- 1/2=sinx. One of the answers is 330-270+30 doesn't equal this. Please help clarify this!