There are an infinite number of solutions, so I don't plan to list them all.
I'll list two of them, and then describe how to get all of the rest.
You said that 2cos(x) - 1 = 0
Add 1 to each side: 2cos(x) = 1
Divide each side by 2: cos(x) = 1/2
The angles whose cosine is 1/2 are 60 degrees, 300 degrees,
and any multiple of 360 degrees added to either of those.
