Simplify (i) `sin(pitan{cot^(-1)((-2)/3)})`
(ii) `sin(2"tan"^(-1)1/2)`
(iii) `cos(2cos^(-1)(1//5)+sin^(-1)(1//5))`

Explanation

Let's simplify the three given expressions step by step.

### (i) Simplify `sin(π * tan(cot^(-1)(-2/3)))`

1. **Let \( y = \tan(\cot^{-1}(-\frac{2}{3})) \)**.
2. **Using the property of cotangent**:
\[
\cot^{-1}(-x) = \pi - \cot^{-1}(x)
...