If `(3pi)/4

Explanation

To solve the problem, we need to simplify the expression \(\sqrt{2 \cot \alpha + \frac{1}{\sin^2 \alpha}}\) and determine its value for \(\alpha\) in the range \(\frac{3\pi}{4} < \alpha < \pi\).

### Step-by-Step Solution:

1. **Start with the given expression:**
\[ \sqrt{2 \cot \alpha + \frac{1}{\sin^2 \alpha}} \]
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