10 Use de Moivre's theorem to express \(\cos 8 \theta\) as a polynomial in \(\cos \theta\).
Hence
- express \(\cos 8 \theta\) as a polynomial in \(\sin \theta\),
- find the exact value of
$$4 x ^ { 4 } - 8 x ^ { 3 } + 5 x ^ { 2 } - x$$
where \(x = \cos ^ { 2 } \left( \frac { 1 } { 8 } \pi \right)\).