Evaluate the following definite integrals
`underset(pi//6)overset(pi//3)intcot^(2)xdx`

Explanation

To evaluate the definite integral \(\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \cot^2 x \, dx\), we will follow these steps:

### Step 1: Rewrite the integrand
We know that \(\cot^2 x = \frac{\cos^2 x}{\sin^2 x}\). Therefore, we can rewrite the integral as:
\[ \int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \cot^2 x \, dx = \int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{\cos^2 x}{\sin^2 x} \, dx \]

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