Trigonometry - Trigonometric Equations

1. Show that \(\sin(x + y)\sin(x - y) \equiv \sin^2 x - \sin^2 y\), for any \(x, y \in \mathbb{R}\).

In triangle \(ABC\), \(a\), \(b\) and \(c\) are the opposite sides of the interior angles \(A\), \(B\) and \(C\), respectively.

2. Hence, show that \(\frac{a^2 - b^2}{c^2} \equiv \frac{\sin(A - B)}{\sin C}\).
3. Given further that \(A\), \(B\) and \(C\) are acute angles and \(b^2 - a^2 = ac\), use the result in (i), or otherwise, find the range of values of \(A\) in terms of \(\pi\).