The equation is equivalent to 1/cos(2x)-2=sin(2x)/cos(2x).
Make the denominator cos(2x) for all terms, we get
1-2cos(2x)=sin(2x).
Since cos^2(2x)+sin^2(2x)=1,
let cos(2x)=a,
substitute sin(2x) by
+-\sqrt(1-a^2),
and solve the equation with only one variable a.
We get a=4/5 or 0,
but cos(2x) cannot be 0,
otherwise sec(2x) is undefined.
2x=36.9 degrees,
so x=18.9 degrees
in radians we have
x=(18.9/180)*pi=0.33
answer
0.33 (it is between [0, 2π))