The diagram shows part of the curve \(y = \frac{1}{16}(3x-1)^2\), which touches the \(x\)-axis at the point \(P\). The point \(Q (3, 4)\) lies on the curve and the tangent to the curve at \(Q\) crosses the \(x\)-axis at \(R\).

(i) State the \(x\)-coordinate of \(P\).

Showing all necessary working, find by calculation

(ii) the \(x\)-coordinate of \(R\),

(iii) the area of the shaded region \(PQR\).