If $12{\cot }^2\theta -31\cos ec\theta +32=0$ , then the value of $\sin \theta$ is

$12\cos e{c}^2\theta -31\cos ec\theta +20=0$

$12\cos c{e}^2\theta -16\cos ec\theta -15\cos ec\theta +20=0$ $$

$4\cos ec\theta \left(3\cos ec\theta -4\right)-5\left(3\cos ec\theta -4\right)=0$

$\left(3\cos ec\theta -4\right)\left(4\cos ce\theta -5\right)=0$

$\cos ec\theta =\frac{4}{3}$ or $\frac{5}{4}$

$\therefore \sin \theta =\frac{3}{4}$  or $\frac{4}{5}$