The first four terms of the binomial expansion of \(( 1 + 2 x ) ^ { 7 }\) in ascending powers of \(x\) are \(1 + a x + b x ^ { 2 } + c x ^ { 3 }\). Find the values of the integers \(a , b\) and \(c\).
Hence find the coefficient of \(x ^ { 3 }\) in the expansion of \(\left( 1 - \frac { 1 } { 2 } x \right) ^ { 2 } ( 1 + 2 x ) ^ { 7 }\).