Finding trigonometric values without using a graph

I really apologise for this stupid question. But around last year I was doing a fmsq mock paper, and it basically asked to find all the values of theta within the range of 0<x<360; so I used the graph method to do it.

After the test my teacher asked me why I used that method, it was correct, but not a quicker way.
To be honest, I can't remember any quicker way to find values that satisfy the range, Could anybody help me?

Graphs are fine - did they mean they wanted you to use CAST?

What is CAST? sorry