The diagram shows the curve \(y = x^3 - 6x^2 + 9x\) for \(x \geq 0\). The curve has a maximum point at \(A\) and a minimum point on the \(x\)-axis at \(B\). The normal to the curve at \(C (2, 2)\) meets the normal to the curve at \(B\) at the point \(D\).

(i) Find the coordinates of \(A\) and \(B\).

(ii) Find the equation of the normal to the curve at \(C\).

(iii) Find the area of the shaded region.