$3 \cos ^{2} 2 \theta+6 \cos 2 \theta-\frac{10(1+\cos 2 \theta)}{2}+5=0$ $\Rightarrow 3 \cos ^{2} 2 \theta+\cos 2 \theta=0$ $\Rightarrow \cos 2 \theta=0$ or $\cos 2 \theta=\frac{-1}{3}$ As $\theta \in[0, \pi], \cos 2 \theta=\frac{-1}{3} \Rightarrow 2$ times $\Rightarrow \theta \in[-4 \pi, 4 \pi], \cos 2 \theta=\frac{-1}{3} \Rightarrow 16$ times Similarly, $\cos 2 \theta=0 \Rightarrow 16$ times $\therefore$ Total 32 solutions