To solve $\tan\left(\frac{2\pi}{3}\right)$, follow these steps:

1. Convert the angle to degrees (optional): $\frac{2\pi}{3} \text{ radians} = \frac{2 \times 180^\circ}{3} = 120^\circ$ However, since the trigonometric functions can be directly computed in radians, this step is not necessary.

2. Use the reference angle: The angle $\frac{2\pi}{3}$ is in the second quadrant. The reference angle is: $\pi - \frac{2\pi}{3} = \frac{\pi}{3}$

3. Evaluate $\tan(\frac{\pi}{3})$: $\tan\left(\frac{\pi}{3}\right) = \sqrt{3}$

4. Determine the sign in the second quadrant: In the second quadrant, tangent is negative. Therefore: $\tan\left(\frac{2\pi}{3}\right) = -\sqrt{3}$

So, the solution is: $\tan\left(\frac{2\pi}{3}\right) = -\sqrt{3}$

Would you like more details on any step, or do you have any questions?

Here are 5 related questions you might find interesting:

1. What is $\tan\left(\frac{4\pi}{3}\right)$?
2. How do you solve $\sin\left(\frac{2\pi}{3}\right)$?
3. What are the trigonometric values for $\pi/3$ in each quadrant?
4. How do you convert between radians and degrees?
5. What is the general solution for $\tan(\theta) = \sqrt{3}$?

Tip: Always remember the signs of trigonometric functions in each quadrant to avoid errors.