Find the value of tan-1 (tan 2π/3) (Answer: -π/3).

Sure, let's solve this step by step:

1. First, we need to understand that the function tan(x) is periodic with a period of π. This means that tan(x) = tan(x + nπ), where n is any integer.

2. The given angle is 2π/3, which is in the second quadrant. The tangent function is positive in the second quadrant.

3. However, the range of tan^-1(x) (inverse tangent function) is from -π/2 to π/2. This means that the output of tan^-1(x) is always in the first or fourth quadrant.

4. Therefore, when we calculate tan^-1(tan(2π/3)), we are actually finding the angle in the first or fourth quadrant that has the same tangent value as 2π/3.

5. Since tan(2π/3) = tan(2π/3 - π) = tan(-π/3), the value of tan^-1(tan(2π/3)) is -π/3.

So, the value of tan^-1(tan(2π/3)) is -π/3.