- (a) Use de Moivre's theorem to prove that
$$\sin 7 \theta = 7 \sin \theta - 56 \sin ^ { 3 } \theta + 112 \sin ^ { 5 } \theta - 64 \sin ^ { 7 } \theta$$
(b) Hence find the distinct roots of the equation
$$1 + 7 x - 56 x ^ { 3 } + 112 x ^ { 5 } - 64 x ^ { 7 } = 0$$
giving your answer to 3 decimal places where appropriate.