Answer
$46.7^{\circ},313.3 ^{\circ}$
Work Step by Step
$2\cos^2{\theta} - 1 + 3 \cos{\theta} - 2 = 0$
$2\cos^2{\theta} + 3 \cos{\theta} - 3 = 0$
Using the quadratic formula:
$\cos{\theta} = \dfrac{-3 \pm \sqrt{9-4(2)(-3)}}{4} = \dfrac{-3\pm \sqrt{33}}{4}$
$\cos{\theta} = \dfrac{-3+\sqrt{33}}{4} \hspace{30pt} \cos{\theta} = \dfrac{-3-\sqrt{33}}{4}$
$\theta = 46.7^{\circ},313.3 ^{\circ}$
