Find the value of `sin(1/2cot^(-1)(-3/4))`

Explanation

To find the value of \( \sin\left(\frac{1}{2} \cot^{-1}\left(-\frac{3}{4}\right)\right) \), we will follow these steps:

### Step 1: Let \( \theta = \cot^{-1}\left(-\frac{3}{4}\right) \)
This means that \( \cot \theta = -\frac{3}{4} \).

### Step 2: Understand the cotangent value
Since \( \cot \theta = \frac{\text{base}}{\text{perpendicular}} \), we can interpret this as:
- Base = -3
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