Solve the equation \(z ^ { 5 } = 1\), giving your answers in polar form.
Hence, by considering the equation \(( z + 1 ) ^ { 5 } = z ^ { 5 }\), show that the roots of
$$5 z ^ { 4 } + 10 z ^ { 3 } + 10 z ^ { 2 } + 5 z + 1 = 0$$
can be expressed in the form \(\frac { 1 } { \mathrm { e } ^ { \mathrm { i } \theta } - 1 }\), stating the values of \(\theta\).