In the binomial expansion of \(\left( 2 x - \frac { 1 } { 2 x } \right) ^ { 5 }\), the first three terms are \(32 x ^ { 5 } - 40 x ^ { 3 } + 20 x\). Find the remaining three terms of the expansion.
Hence find the coefficient of \(x\) in the expansion of \(\left( 1 + 4 x ^ { 2 } \right) \left( 2 x - \frac { 1 } { 2 x } \right) ^ { 5 }\).
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The diagram shows triangle \(A B C\) which is right-angled at \(A\). Angle \(A B C = \frac { 1 } { 5 } \pi\) radians and \(A C = 8 \mathrm {~cm}\). The points \(D\) and \(E\) lie on \(B C\) and \(B A\) respectively. The sector \(A D E\) is part of circle with centre \(A\) and is such that \(B D C\) is the tangent to the \(\operatorname { arc } D E\) at \(D\).