To solve the equation $2 \cos(\theta) + \sqrt{3} = 0$, follow these steps:

1. Rearrange the equation: $2 \cos(\theta) = -\sqrt{3}$

2. Divide both sides by 2: $\cos(\theta) = -\frac{\sqrt{3}}{2}$

3. Find the reference angle: The reference angle for $\cos(\theta) = \frac{\sqrt{3}}{2}$ is $\theta = \frac{\pi}{6}$.

4. Determine the quadrants: Since $\cos(\theta) = -\frac{\sqrt{3}}{2}$, $\theta$ is in the second and third quadrants.

5. Calculate the angles:

   • Second quadrant: $\theta = \pi - \frac{\pi}{6} = \frac{5\pi}{6}$
   • Third quadrant: $\theta = \pi + \frac{\pi}{6} = \frac{7\pi}{6}$

6. General solution: The general solutions are: $\theta = \frac{5\pi}{6} + 2k\pi, \frac{7\pi}{6} + 2k\pi$ where $k$ is any integer.

The solutions are $\frac{5\pi}{6} + 2k\pi, \frac{7\pi}{6} + 2k\pi$.