Find the principal value of each of the following:
(i) `sin^(-1)(-(sqrt(3))/2)`
(ii) `sin^(-1)(cos(2pi)/3)`
(iii) `sin^(-1)((sqrt(3)-1)/(2sqrt(2)))`

Explanation

To find the principal values of the given inverse trigonometric functions, we will solve each part step by step.

### (i) Find `sin^(-1)(-(sqrt(3))/2)`

1. **Identify the angle whose sine is `-(sqrt(3))/2`:**
The sine function is negative in the fourth quadrant. The reference angle for `sqrt(3)/2` is `pi/3`. Therefore, the angle in the fourth quadrant is `-pi/3`.

2. **Write the principal value:**
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