The diagram shows part of the curve \(y = (x - 2)^4\) and the point \(A (1, 1)\) on the curve. The tangent at \(A\) cuts the \(x\)-axis at \(B\) and the normal at \(A\) cuts the \(y\)-axis at \(C\).

1. Find the coordinates of \(B\) and \(C\).
2. Find the distance \(AC\), giving your answer in the form \(\frac{\sqrt{a}}{b}\), where \(a\) and \(b\) are integers.
3. Find the area of the shaded region.