- (a) Use de Moivre's theorem to show that
$$\tan 4 \theta \equiv \frac { 4 \tan \theta - 4 \tan ^ { 3 } \theta } { 1 - 6 \tan ^ { 2 } \theta + \tan ^ { 4 } \theta }$$
(b) Use the identity given in part (a) to find the 2 positive roots of
$$x ^ { 4 } + 2 x ^ { 3 } - 6 x ^ { 2 } - 2 x + 1 = 0$$
giving your answers to 3 significant figures.
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