cos(2x)=1-2sin2(x),
cos(2x)-2sin2(x)=1-2sin2(x)-2sin2(x)=1-4sin2(x).
If cos(2x)-2sin2(x)=0, 1-4sin2(x)=0, (1-2sin(x))(1+2sin(x))=0,
so sin(x)=½ or -½. Therefore x=π/6 (30°), 5π/6 (150°), 7π/6 (210°), 11π/6 (330°).
There are other solutions found by adding multiples of 2π or 360° to each of these.