Find the value of:
i) `sin^(-1)(sin (2pi)/3))`,
ii) `cos^(-1)(cos(7pi)/6)`,
iii) `tan^(-1)(tan(3pi)/4)`

Explanation

To solve the given problems, we will evaluate each expression step by step, ensuring that we respect the principal values of the inverse trigonometric functions.

### i) Find the value of `sin^(-1)(sin(2π/3))`

1. **Identify the angle**: The angle given is \( \frac{2\pi}{3} \).
2. **Check the principal range**: The principal range for \( \sin^{-1}(x) \) is \( [-\frac{\pi}{2}, \frac{\pi}{2}] \). Since \( \frac{2\pi}{3} \) is not in this range, we need to find an equivalent angle within the principal range.
3. **Convert to principal value**: We can express \( \frac{2\pi}{3} \) as \( \pi - \frac{\pi}{3} \). Thus, \( \sin\left(\frac{2\pi}{3}\right) = \sin\left(\pi - \frac{\pi}{3}\right) = \sin\left(\frac{\pi}{3}\right) \).
4. **Evaluate the sine**: We know that \( \sin\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2} \).
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