Answer:
or
Explanation:
See attached. I know (very haphazard). But the basic method is to inverse the trig function. This gives you the position of the terminal angle. -45 degrees means that you turned 45 degrees clockwise and are in quadrant 4. This corresponds to an angle of rotation of 315 degrees counter clockwise which is what we are looking for since the specified domain is betwern 0 and 360 degrees or 0 and 2 pi.
The next thing to remember is that Tan is also negative in Quadrant 2 (using the ASTC rule). This corresponds to an angle of rotation of 180 - 45 = 135 degrees.
Hope that helps.