2) sin30 = 1/2 and cos30 = (sqrt3)/2 (note: sqrt = sqare root) so 1/2cosx - (sqrt3)/2sinx = sinx
3) Bring the sin values over onto one side of the eqation: 1/2 cosx = (2+sqrt3)/2 sinx.
4) (optional) Multiply both sides by 2 to remove the denominator: cosx = (2+sqrt3) sinx.
5) sinx / cosx = tanx so divide both sides by cosx: 1 = ((2+sqrt3) sinx) / cosx = (2+sqrt3) tanx.
6) Divide both sides by (2+sqrt3): 1/(2+sqrt3) = tanx.
7) Take the arctan of both sides (aka tan^-1 / inverse tan): tan^-1( 1/(2+sqrt3) ) = tan^-1(tanx) = x = 75.
8) Solve for x in the given interval. E.g. for 0 =< x <= 360, there are 2 solutions: 75 degrees and 75+180 = 255 degrees. You may find it helpful to draw the tangent graph and see where the solutions came from graphically.