Question:

Find all the values of $\displaystyle x$ in the interval $\displaystyle 0^o \leq x \leq 180^o$ which satisfy the equation $\displaystyle \sin{3x} + 2\cos{3x} = 0.$

Attempt:

$\displaystyle \sin{3x} + 2\cos{3x} = 0.$

$\displaystyle \sin{3x} = -2\cos{3x}$

$\displaystyle \frac{\sin{3x}}{\cos{3x}} = -2$

$\displaystyle \tan{3x} = -2$

$\displaystyle 3x = \tan^{-1}(-2)$

Calculator gives no value for $\displaystyle \tan^{-1}(-2)$, need help.