Find the principal values of the following
(i) `tan^(-1) (tan. (2pi)/(3))` (ii) `tan^(-1) (tan (-6))`

Explanation

To solve the given problems, we will find the principal values of the inverse tangent function applied to the tangent of specific angles.

### (i) Find `tan^(-1)(tan(2π/3))`

1. **Identify the angle**: The angle given is \( \frac{2\pi}{3} \).
2. **Check the principal value range**: The principal value of the \( \tan^{-1} \) function is in the range \( \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \). Since \( \frac{2\pi}{3} \) is not in this range, we need to convert it.
3. **Use the property of tangent**: We know that \( \tan(\pi - \theta) = -\tan(\theta) \). Thus, we can write:
\[
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