Divide both sides by 4 to get
[tex]\tan(3x)=-1[/tex]
Recalling the definition of tangent as ratio between sine and cosine, we have
[tex]\tan(3x)=-1 \iff \dfrac{\sin(3x)}{\cos(3x)}=-1 \iff \sin(3x)=-\cos(3x)[/tex]
The sine and cosine of an angle are opposite only if the angle is
[tex]\alpha = 135+180k,\quad k \in \mathbb{Z}[/tex]
So, we have
[tex]3x=135+180k \iff x = 45+60k,\quad k \in \mathbb{Z}[/tex]
So, the solutions are
[tex]\alpha \in \{45,\ 105,\ 165,\ 225,\ 285,\ 345\}[/tex]
