Use a trigonometric identity to rewrite the equation. Then expand and combine like terms to form a trinomial. Then solve the trinomial by factoring.
Solve the equation \(6\tan^2 \theta + 13\sec \theta = 2\) for \(0^\circ \le \theta \le 360^\circ.\)
Solve the equation \(2\sin^2 x + 3\sin x + 1 = 0\) for \(0 \le x \lt 2\pi.\)
Solve the equation \(\sin^2 x = 3\cos^2 x\) for \(0 \le x \lt 2\pi.\)
Find all angles between \(0\) and \(2\pi\) which satisfy the equation \(2\sin^2 x = 5\cos x - 1.\)