1. **State the problem:** Solve the equation $$y = 3 \sin^2(x - \pi)$$ for $y$ in terms of $x$. 2. **Recall the formula and rules:** The function involves the square of the sine function. We use the identity $$\sin^2 \theta = \frac{1 - \cos(2\theta)}{2}$$ to simplify. 3. **Apply the identity:** $$y = 3 \sin^2(x - \pi) = 3 \cdot \frac{1 - \cos(2(x - \pi))}{2}$$ 4. **Simplify inside the cosine:** $$\cos(2(x - \pi)) = \cos(2x - 2\pi)$$ 5. **Use the periodicity of cosine:** Since $$\cos(\alpha - 2\pi) = \cos \alpha$$, $$\cos(2x - 2\pi) = \cos(2x)$$ 6. **Substitute back:** $$y = \frac{3}{2} (1 - \cos(2x))$$ 7. **Final simplified form:** $$\boxed{y = \frac{3}{2} - \frac{3}{2} \cos(2x)}$$ This expresses $y$ in terms of $x$ using a simpler trigonometric form.