The diagram shows part of the curve \(y = \frac{3}{\sqrt{1 + 4x}}\) and a point \(P(2, 1)\) lying on the curve. The normal to the curve at \(P\) intersects the \(x\)-axis at \(Q\).

(i) Show that the \(x\)-coordinate of \(Q\) is \(\frac{16}{9}\).

(ii) Find, showing all necessary working, the area of the shaded region.