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The diagram shows part of the curve \(y = 2 ( 3 x - 1 ) ^ { - \frac { 1 } { 3 } }\) and the lines \(x = \frac { 2 } { 3 }\) and \(x = 3\). The curve and the line \(x = \frac { 2 } { 3 }\) intersect at the point \(A\).
- Find, showing all necessary working, the volume obtained when the shaded region is rotated through \(360 ^ { \circ }\) about the \(x\)-axis.
- Find the equation of the normal to the curve at \(A\), giving your answer in the form \(y = m x + c\).