1. The problem is to find the value of $\cos\left(\frac{2\pi}{3}\right)$.\n\n2. Recall that the cosine function for an angle $\theta$ in radians gives 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, where cosine values are negative.\n\n4. We use the reference angle $\pi - \frac{2\pi}{3} = \frac{\pi}{3}$. The cosine of $\frac{2\pi}{3}$ is the negative cosine of $\frac{\pi}{3}$.\n\n5. We know $\cos\left(\frac{\pi}{3}\right) = \frac{1}{2}$.\n\n6. Therefore, $\cos\left(\frac{2\pi}{3}\right) = -\frac{1}{2}$.\n\nFinal answer: $\boxed{-\frac{1}{2}}$.