$3 \tan\left(\dfrac x 2\right)+3=0$

$3 \tan\left(\dfrac x 2\right)=-3$

$\tan\left(\dfrac x 2\right)=-1$

$\dfrac x 2 =\arctan(-1)$

$\dfrac x 2 = \dfrac {3\pi}{4} + 2k\pi~~k\in \mathbb{Z}$

OR

$\dfrac x 2 = \dfrac {7\pi}{4} + 2k\pi~~k\in \mathbb{Z}$

$x = \dfrac{3\pi}{2}+4k\pi~~k\in \mathbb{Z}$

OR

$x = \dfrac{7\pi}{2}+4k\pi~~k\in \mathbb{Z}$