Answer
$positive$, $III$, $30^\circ$, $\frac{\sqrt 3}{3}$.
Work Step by Step
We can identify $\theta=-150^\circ$ to be in quadrant $III$, thus $tan\theta$ will be $positive$. The reference angle is the acute angle formed by the terminal line with x-axis and it can be found as $180^\circ-150^\circ=30^\circ$, thus the exact value is $tan(-150^\circ)=tan30^\circ=\frac{\sqrt 3}{3}$.
The answers are $positive$, $III$, $30^\circ$, $\frac{\sqrt 3}{3}$.
