2. Let vector $\vec{a}=\{\sin 2 \varphi, 1, \tan \varphi\}, \vec{b}=\{1, \cos \varphi, \cot \varphi\}, \varphi \in[0,2 \pi)$. If $\vec{a} \cdot \vec{b}=1$, then the value of $\varphi$ is ( ).
A. $\frac{\pi}{2}, \frac{7 \pi}{6}$
B. $\frac{3 \pi}{2}, \frac{11 \pi}{6}$
C. $\frac{7 \pi}{6}, \frac{11 \pi}{6}$
D. $\frac{\pi}{2}, \frac{3 \pi}{2}, \frac{7 \pi}{6}, \frac{11 \pi}{6}$
2. C. $\sin 2 \varphi+\cos \varphi+1=1$, i.e., $\cos \varphi(2 \sin \varphi+1)=0$, so $\sin \varphi=-\frac{1}{2}$.