If the set of all values of `x` in `(-pi/2,pi/2)` satisfying |4sinx+`sqrt(2 )`|<`sqrt(6)` then find the value of `x`

Explanation

To solve the inequality \( |4\sin x + \sqrt{2}| < \sqrt{6} \) for \( x \) in the interval \( (-\frac{\pi}{2}, \frac{\pi}{2}) \), we will follow these steps:

### Step 1: Remove the absolute value
The inequality \( |4\sin x + \sqrt{2}| < \sqrt{6} \) can be rewritten as two separate inequalities:
\[ -\sqrt{6} < 4\sin x + \sqrt{2} < \sqrt{6} \]

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