For any angle \(\small \theta\), the following are true:
$$ \sin(2\theta) = 2 \sin(\theta) \cos(\theta) $$
$$ \small \cos(2\theta) = \cos^2(\theta) - \sin^2(\theta) = 2 \cos^2(\theta) - 1 = 1 - 2 \sin^2(\theta)$$
$$ \tan(2\theta) = \frac{2 \tan(\theta)}{1 - \tan^2(\theta)} $$
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