Find all solutions of the equation in the interval $[0,2 \pi)$.
\[
\cot \theta+\sqrt{3}=0
\]

Step 1 ：We can write the equation as \[\frac{1}{\tan \theta} + \sqrt{3} = 0.\]

Step 2 ：Then \[\frac{1}{\sin \theta / \cos \theta} + \sqrt{3} = 0.\]

Step 3 ：Multiplying through by \(\cos \theta\), we get \[1 + \sqrt{3} \cos \theta = 0.\]

Step 4 ：Rearranging, we find \[\cos \theta = -\frac{1}{\sqrt{3}}.\]

Step 5 ：Since \(\cos \theta\) is negative, \(\theta\) must be in the second or third quadrant. In the interval \([0,2 \pi)\), the solutions are \[\theta = \frac{2\pi}{3}\] and \[\theta = \frac{4\pi}{3}.\]

Step 6 ：We check that both solutions work in the original equation. For \(\theta = \frac{2\pi}{3}\), \[\cot \theta + \sqrt{3} = \frac{\cos \theta}{\sin \theta} + \sqrt{3} = -\frac{1}{\sqrt{3}} + \sqrt{3} = 0.\] For \(\theta = \frac{4\pi}{3}\), \[\cot \theta + \sqrt{3} = \frac{\cos \theta}{\sin \theta} + \sqrt{3} = -\frac{1}{\sqrt{3}} + \sqrt{3} = 0.\]

Step 7 ：So the solutions are \[\boxed{\theta = \frac{2\pi}{3}, \frac{4\pi}{3}}.\]