The diagram shows part of the curve \(y=(x+2)^2(1-3x)\). The curve has a minimum point \(A\) and a maximum point \(B\). The curve intersects the \(y\)-axis at \(C\) and the \(x\)-axis at \(D\).

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

(ii) Find the coordinates of \(C\) and \(D\).

(iii) Find the area of the shaded region.