$2 \operatorname{arccot}\left(-\frac{1}{2}\right)+\operatorname{arccot}(-2)$ equals
A. $-\frac{\pi}{2}$
B. $\frac{3 \pi}{4}$
C. $\frac{3 \pi}{2}$
D. $2 \pi$
$2 \mathrm{C}$.
$$
\begin{aligned}
\operatorname{arccot}\left(-\frac{1}{2}\right)+\operatorname{arccot}(-2) & =\pi-\operatorname{arccot} \frac{1}{2}+\pi-\operatorname{arccot} 2 \\
& =2 \pi-(\arctan 2+\operatorname{arccot} 2) \\
& =2 \pi-\frac{\pi}{2}=\frac{3 \pi}{2} .
\end{aligned}
$$