Help finding all solutions of sec^2x + tanx - 3 = 0 in the interval [0, 2pi)

sec^2x + tanx - 3 = 0
tan^2x + 1 + tanx - 3 = 0
tan^2x + tanx - 2 = 0
(tanx + 2)(tanx - 1) = 0
tanx = -2 or tanx = 1
x = 2.034 radians or x = 5.176 radians or x = pi/4 radians or x = 5pi/4 radians