3.381. Find $\cos 2 \alpha$, if it is known that $2 \operatorname{ctg}^{2} \alpha+7 \operatorname{ctg} \alpha+3=0$ and the number $\alpha$ satisfies the inequalities: a) $\frac{3 \pi}{2}<\alpha<\frac{7 \pi}{4}$; b) $\frac{7 \pi}{4}<\alpha<2 \pi$.