Explanation

(c)
Since,$\ \left( 2\tan{\theta + 2} \right)^{2} = \tan{\theta\left( 3\tan{\theta + 3} \right)}$
$\Rightarrow 4\tan^{2}{\theta + 8\ tan\ \theta + 4 = 3\tan^{2}{\theta + 3\tan\theta}}$
$\Rightarrow \tan^{2}{\theta + 5\tan{\theta + 4 = 0}}$
$\Rightarrow \left( \tan{\theta + 4} \right)\left( \tan{\theta + 1} \right) = 0$
$\Rightarrow \tan{\theta = - 4\ \ \left( \because\tan{\theta \neq - 1} \right)}$
$\therefore\frac{7 - 5\cot\theta}{9 - 4\sqrt{\tan^{2}\theta}} = \ \frac{7 + \frac{5}{4}}{9 - 4( - 4)} = \frac{33}{100}$