Step 1 :The problem is to find the value of \(\tan \left(\frac{2 \pi}{3}\right)\).
Step 2 :The tangent function is defined as the ratio of the sine to the cosine of an angle.
Step 3 :In the unit circle, the angle \(\frac{2 \pi}{3}\) is in the second quadrant where sine is positive and cosine is negative.
Step 4 :Therefore, the tangent of this angle will be negative.
Step 5 :The exact value of \(\tan \left(\frac{2 \pi}{3}\right)\) is approximately -1.732, which is the square root of 3.
Step 6 :So, the tangent of \(\frac{2 \pi}{3}\) is \(-\sqrt{3}\).
Step 7 :Final Answer: \(\boxed{-\sqrt{3}}\)