find all solutions of the equation in the interval 02pi tan2

find all solutions of the equation in the interval [0,2pi)

tan^2x-secx=1

write your answer in radians in terms of pi

tan^2x - secx = 1

sec^2 x - sec x - 2 = 0

Let sec x = y

Then y^2 - y - 2 = 0

y = sec x = 2 ======> cos x = 1/2 =====> x = pi/3, 5pi/3

y = sec x = -1 =====> cos x = -1 =====> x = pi