(a) Start by putting the expression over a single common denominator:

\(\frac{\sin \theta (1 + \sin \theta) - \sin \theta (1 - \sin \theta)}{(1 - \sin \theta)(1 + \sin \theta)}\)

This simplifies to:

\(\frac{\sin \theta + \sin^2 \theta - \sin \theta + \sin^2 \theta}{1 - \sin^2 \theta}\)

\(= \frac{2 \sin^2 \theta}{\cos^2 \theta}\)

\(= 2 \tan^2 \theta\)

(b) From part (a), we have:

\(2 \tan^2 \theta = 8\)

\(\tan^2 \theta = 4\)

\(\tan \theta = \pm 2\)

Solving for \(\theta\) in the range \(0^\circ < \theta < 180^\circ\), we find:

\(\theta = 63.4^\circ, \ 116.6^\circ\)