$\sin{3\theta} \,=\, 3\sin{\theta}-4\sin^3{\theta}$

$\cos{3\theta} \,=\, 4\cos^3{\theta}-3\cos{\theta}$

$\tan{3\theta} \,=\, \dfrac{3\tan{\theta}-\tan^3{\theta}}{1-3\tan^2{\theta}}$

$\cot{3\theta} \,=\, \dfrac{3\cot{\theta}-\cot^3{\theta}}{1-3\cot^2{\theta}}$

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