In order to determine the graph of the given function, cosider:
The function f(x) is indetermined when the argument of the cot is 0.
[tex]\begin{gathered} x+\frac{\pi}{6}=0 \\ x=-\frac{\pi}{6} \end{gathered}[/tex]
In this case, the period is 2pi. Then, not only for x=-pi/6, but for x=5pi/6 the function is indeterminate.
Then, the graph is:
