Answer
$\dfrac{\sqrt{3}}{3}$
Work Step by Step
RECALL:
(1)The reference angle of a given angle is equal to the smallest acute angle that the terminal side makes with the x-axis.
(2) Based on the location of the terminal side of an angle $\theta$, the reference angle can be found using the formula:
(i) Quadrant I: $\theta$
(ii) Quadrant II: $180^0-\theta$
(iii) Quadrant III: $\theta-180^o$
(iv) Quadrant IV: $360^o-\theta$
The given angle is in Quadrant III.
Use the formula in (iii) above to find its reference angle:
$=210^0-180^o
\\=30^o$
Note that $210^o$ is i Quadrant III, where tangent is positive.
Thus,
$\tan{210^o} = \tan{30^o}$
$30^o$ is a special angle whose tangent value is $\dfrac{\sqrt{3}}{3}$.
Thus,
$\tan{210^o} = \dfrac{\sqrt{3}}{3}$
