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Prove It Well for the first, you'll need to make use of the following identities:
$\displaystyle \displaystyle \begin{align*} \tan{x} &\equiv \frac{\sin{x}}{\cos{x}} \\ \\ \sin{2x} &\equiv 2\sin{x}\cos{x} \\ \\ \cos{2x} &\equiv \cos^2{x} - \sin^2{x} \\ \\ \sin^2{x} + \cos^2{x} &\equiv 1 \\ \\ \tan{\left(\alpha + \beta\right)} &\equiv \frac{\tan{\alpha} + \tan{\beta}}{1 - \tan{\alpha}\tan{\beta}}\end{align*}$
Start by writing $\displaystyle \displaystyle \begin{align*} \tan{3\theta} = \tan{\left(2\theta + \theta\right)}\end{align*}$. What do you think you would do from here?