1. The problem is to evaluate $\cos \frac{2\pi}{3}$.\n\n2. Recall that the cosine function for an angle $\theta$ in radians is the x-coordinate of the point on the unit circle at that angle.\n\n3. The angle $\frac{2\pi}{3}$ radians is in the second quadrant (between $\frac{\pi}{2}$ and $\pi$).\n\n4. The reference angle for $\frac{2\pi}{3}$ is $\pi - \frac{2\pi}{3} = \frac{\pi}{3}$.\n\n5. We know $\cos \frac{\pi}{3} = \frac{1}{2}$.\n\n6. In the second quadrant, cosine values are negative, so $\cos \frac{2\pi}{3} = -\cos \frac{\pi}{3} = -\frac{1}{2}$.\n\n7. Therefore, the value of $\cos \frac{2\pi}{3}$ is $-\frac{1}{2}$.