1 Given that \(z = 2 \mathrm { e } ^ { \frac { \pi \mathrm { i } } { 12 } }\) satisfies the equation
$$z ^ { 4 } = a ( 1 + \sqrt { 3 } i )$$
where \(a\) is real:
- find the value of \(a\);
- find the other three roots of this equation, giving your answers in the form \(r \mathrm { e } ^ { \mathrm { i } \theta }\), where \(r > 0\) and \(- \pi < \theta \leqslant \pi\).