The function \(f : x \mapsto 5 \sin^2 x + 3 \cos^2 x\) is defined for the domain \(0 \leq x \leq \pi\).

1. Express \(f(x)\) in the form \(a + b \sin^2 x\), stating the values of \(a\) and \(b\).
2. Hence find the values of \(x\) for which \(f(x) = 7 \sin x\).
3. State the range of \(f\).