Let's simplify the integrand before evaluating the integral:

\(\int_{0}^{\pi} \frac{\cos^2\theta - 1}{\sin^2\theta} \, d\theta\)

Using the trigonometric identity \(\cos^2\theta = 1 - \sin^2\theta\), we can rewrite the integrand:

\(\int_{0}^{\pi} \frac{1 - \sin^2\theta - 1}{\sin^2\theta} \, d\theta\)

Simplify the numerator:

\(\int_{0}^{\pi} \frac{-\sin^2\theta}{\sin^2\theta} \, d\theta\)

Since \(\sin^2\theta\) cancels out, the integral becomes:

\(\int_{0}^{\pi} -1 \, d\theta\)

Now, integrate with respect to \(\theta\):

\(-\int_{0}^{\pi} 1 \, d\theta = -\left[\theta\right]_{0}^{\pi} = -(\pi - 0) = -\pi\)

Therefore, the value of the integral is \(-\pi\).