9. (2004 National College Entrance Examination - Guangdong Paper) Given: $\alpha, \beta, \gamma$ are terms of a geometric sequence with a common ratio of 2 $(\alpha \in[0,2 \pi])$. Also, $\sin \alpha, \sin \beta, \sin \gamma$ form a geometric sequence. Find the values of $\alpha, \beta, \gamma$.
9. $\alpha=\frac{2}{3} \pi, \beta=\frac{4}{3} \pi, \gamma=\frac{8}{3} \pi$ or $\alpha=\frac{4}{3} \pi, \beta=\frac{8}{3} \pi, \gamma=\frac{16}{3} \pi . \beta=2 \alpha, \gamma=4 \alpha$. Also, $\frac{\sin 2 \alpha}{\sin \alpha}=\frac{\sin 4 \alpha}{\sin 2 \alpha}$, so $\cos \alpha=\cos 2 \alpha=2 \cos ^{2} \alpha-1 \Rightarrow \cos \alpha=1$ or $\cos \alpha=-\frac{1}{2}$. When $\cos \alpha=1$, $\sin \alpha=0$. The first term of the geometric sequence is not 0, so we discard this. When $\cos \alpha$ $=-\frac{1}{2}$, $\alpha=\frac{2}{3} \pi$ or $\alpha=\frac{4}{3} \pi$ so $\beta=\frac{4}{3} \pi, \gamma=\frac{8}{3} \pi$ or $\beta=\frac{8}{3} \pi, \gamma=\frac{16}{3} \pi$