The first term \(a = \sin^2 \theta\).

The second term \(ar = \sin^2 \theta \cos^2 \theta\).

Thus, the common ratio \(r = \cos^2 \theta\).

The sum to infinity of a geometric progression is given by:

\(S_\infty = \frac{a}{1-r}\)

Substitute \(a = \sin^2 \theta\) and \(r = \cos^2 \theta\):

\(S_\infty = \frac{\sin^2 \theta}{1 - \cos^2 \theta}\)

Since \(1 - \cos^2 \theta = \sin^2 \theta\), we have:

\(S_\infty = \frac{\sin^2 \theta}{\sin^2 \theta} = 1\)