Draw $\displaystyle{{210}}^{\circ}\usepackage{cmbright}\Huge\$ in standard position. The terminal side is in the third quadrant and the reference angle is $\displaystyle{{30}}^{\circ}\usepackage{cmbright}\Huge\$ . Use the $\displaystyle{{30}}^{\circ}-{{60}}^{\circ}-{{90}}^{\circ}\usepackage{cmbright}\Huge\$ triangle to find the value of this function at the reference angle:

$\displaystyle{{\tan{{30}}}}^{\circ}=\frac{{1}}{\sqrt{{3}}}=\frac{{1}}{\sqrt{{3}}}\cdot\frac{\sqrt{{3}}}{\sqrt{{3}}}=\frac{\sqrt{{3}}}{{3}}\usepackage{cmbright}\Huge\$

Use the signs of x and y in the third quadrant to determine the sign of tangent:

$\displaystyle{{\tan{{210}}}}^{\circ}=\frac{{y}}{{x}}=\frac{{{\left(-\right)}}}{{{\left(-\right)}}}={\left(+\right)}\usepackage{cmbright}\Huge\$

So: $\displaystyle{{\tan{{210}}}}^{\circ}=+\frac{\sqrt{{3}}}{{3}}\usepackage{cmbright}\Huge\$