(a) Start with the given equation:

\(\sin 2\theta + \cos 2\theta = 2 \sin^2 \theta\)

Using double angle identities, we have:

\(\sin 2\theta = 2 \sin \theta \cos \theta\)

\(\cos 2\theta = \cos^2 \theta - \sin^2 \theta\)

Substitute these into the equation:

\(2 \sin \theta \cos \theta + \cos^2 \theta - \sin^2 \theta = 2 \sin^2 \theta\)

Rearrange terms:

\(\cos^2 \theta + 2 \sin \theta \cos \theta - 3 \sin^2 \theta = 0\)

(b) Factor the equation:

\((\cos \theta - \sin \theta)(\cos \theta + 3 \sin \theta) = 0\)

Set each factor to zero:

\(\cos \theta - \sin \theta = 0\)

\(\tan \theta = 1\)

\(\theta = 45^\circ\)

And:

\(\cos \theta + 3 \sin \theta = 0\)

\(\tan \theta = -\frac{1}{3}\)

\(\theta \approx 161.6^\circ\)

Thus, the solutions are \(\theta = 45^\circ\) and \(\theta \approx 161.6^\circ\).