Find all solutions in the interval [0, 2π).

sec2 x - 2 = tan2 x

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 approximately.