Solve the equation over the interval \( [0,2 \pi) \). \[ \cot \beta=\sqrt{3} \]

Step 1: Rewrite the equation \(\cot \beta = \sqrt{3}\) in terms of tangent: \(\tan \beta = \frac{1}{\sqrt{3}}\). Step 2: Identify the angles where \(\tan \beta = \frac{1}{\sqrt{3}}\). This occurs at \(\beta = \frac{\pi}{6}\) and in the third quadrant at \(\beta = \frac{7\pi}{6}\). Step 3: Ensure both solutions are within the interval \([0, 2\pi)\). Step 4: Conclude with the two solutions: \(\beta = \frac{\pi}{6}\) and \(\beta = \frac{7\pi}{6}\).