C3 Trig equation - huh?

[tfortola]

Solve, showing clear working and giving your answers in radians to two decimal places,

6sec 2x + 5tan 2x = 12 0 ≤ x ≥ pi

[DaveD]

6sec 2x + 5tan 2x = 12 0 ≤ x ≥ pi
Use the identity 1+tan A = sec A
6(1+tan 2x) +5tan 2x = 12

6+6tan 2x +5tan 2x - 12=0
6tan 2x +5tan 2x - 6=0
(3tan 2x -2)(2tan 2x -3) = 0
3 tan 2x = 2 or 2 tan 2x = 3
tan2x = 2/3 or tan 2x =3/2
2x = inv tan 2/3 or 2x = inv tan 3/2
2x = .588, 3.729 or 0.9823, 4.124
x=0.294, 1.865, 0.491 ,2.06