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**Jhevon** Hint: Use the addition formulas for tangent

recall: $\displaystyle \tan ( \alpha + \beta ) = \frac {\tan \alpha + \tan \beta }{1 - \tan \alpha \tan \beta}$ and $\displaystyle \tan ( \alpha - \beta ) = \frac {\tan \alpha - \tan \beta}{1 + \tan \alpha \tan \beta}$

use the double angle formula for sine

$\displaystyle \sin 2x + \cos x = 0$

$\displaystyle \Rightarrow 2 \sin x \cos x + \cos x = 0$

$\displaystyle \Rightarrow \cos x ( 2 \sin x + 1 ) = 0$

Now continue

use the double angle formula for tangent

$\displaystyle 3 \tan x = \tan 2x$

$\displaystyle \Rightarrow 3 \tan x = \frac {2 \tan x }{1 - \tan^2 x}$

Now continue.