To determine which fundamental identity is used in the proof, let's first analyze the left-hand side of the given equation:
\[ \sin^2 \theta - \cos^2 \theta \sin^2 \theta \]
This expression can be factored as follows:
\[ \sin^2 \theta (1 - \cos^2 \theta) \]
Next, we recall the Pythagorean identity:
\[ \sin^2 \theta + \cos^2 \theta = 1 \]
From this identity, we can deduce that:
\[ 1 - \cos^2 \theta = \sin^2 \theta \]
Substituting this back into the factored expression gives:
\[ \sin^2 \theta \cdot \sin^2 \theta = \sin^4 \theta \]
Thus, the identity used in the second step of the proof is:
\[ \sin^2 \theta + \cos^2 \theta = 1 \]
So the correct answer is:
sine squared theta plus cosine squared theta equals 1.