you can use the pythagorean substitution. Since Cos2 x + Sin2 x = 1, Sin2 x = 1-cos2 x.
So you have 2 cos x -(1-cos2 x) = cos2 x
2cos x - 1 + cos2 x = cos2x
2cos x -1 = 0
cos x = 1/2
Since cosine is positive, you have an answer in the first and the other in the fourth quadrant.
You can use a calculator to find the one in the first quadrant, or use the 30-60-90 to find that x = 60 = Π/3.
A 60 degree reference angle in the fourth quadrant would be a 300 degree angle....or 5π/3.
Hope this helped.