Explanation

(c)
Given, $2\sin^{2}{\theta + \sqrt{3}\cos{\theta + 1 = 0}}$
$\Rightarrow \ 2\cos^{2}{\theta - \sqrt{3}\cos{\theta - 3 = 0}}$
$\therefore\ \ \ \cos{\theta = \frac{\sqrt{3} \pm \sqrt{3 + 4 \times 3 \times 2}}{2 \times 2}}$
$= \frac{\sqrt{3} \pm 3\sqrt{3}}{4}$
$\Rightarrow \ \cos{\theta = - \frac{\sqrt{3}}{2}}$ [$\because\cos{\theta \neq \sqrt{3}}$]
$\Rightarrow \ \ \ \theta = \frac{5\pi}{6}$