ANSWER
[tex] \boxed { \sqrt{} }30 \degree[/tex]
[tex] \boxed { \sqrt{} }210 \degree[/tex]
EXPLANATION
We want to solve
[tex] \cot( \theta) = \sqrt{3} [/tex]
where
[tex]0 \degree \: \leqslant x \leqslant 360 \degree[/tex]
We reciprocate both sides of this trigonometric equation to obtain:
[tex] \tan( \theta) = \frac{1}{ \sqrt{3} } [/tex]
We take arctangent of both sides to get;
[tex] \theta = \tan ^{ - 1} ( \frac{1}{ \sqrt{3} } ) [/tex]
[tex] \theta = 30 \degree[/tex]
This is the principal solution.
The tangent ratio is also positive in the third quadrant.
The solution in the third quadrant is
[tex]180 + \theta = 180 + 30 = 210 \degree[/tex]
