To determine which angle has its terminal side in the third quadrant, we need to know the ranges for angles in standard position:
- The angles in the third quadrant are between \(\pi\) and \(\frac{3\pi}{2}\) (or between 180 degrees and 270 degrees).
Now let's evaluate each of the given angles:
- \(\frac{3\pi}{4}\): This is in the second quadrant (between \(\frac{\pi}{2}\) and \(\pi\)).
- \(\frac{\pi}{3}\): This is in the first quadrant (between \(0\) and \(\frac{\pi}{2}\)).
- \(\frac{5\pi}{3}\): This is in the fourth quadrant (between \(\frac{3\pi}{2}\) and \(2\pi\)).
- \(\frac{7\pi}{6}\): This is in the third quadrant (between \(\pi\) and \(\frac{3\pi}{2}\)).
Therefore, the angle that has its terminal side in the third quadrant is:
\(\frac{7\pi}{6}\).