Using the definition of \(\sinh x\) in terms of \(\mathrm { e } ^ { x }\) and \(\mathrm { e } ^ { - x }\), show that
$$4 \sinh ^ { 3 } x = \sinh 3 x - 3 \sinh x$$
\section*{(ii) In this question you must show detailed reasoning.}
By making a suitable substitution, find the real root of the equation
$$16 u ^ { 3 } + 12 u = 3 .$$
Give your answer in the form \(\frac { \left( a ^ { \frac { 1 } { b } } - a ^ { - \frac { 1 } { b } } \right) } { c }\) where \(a , b\) and \(c\) are integers.