Find the values of x in the interval `[0,2pi]` for which `4sin^(2)x - 8 sinx+3 le0`

Explanation

To solve the inequality \( 4\sin^2 x - 8\sin x + 3 \leq 0 \), we will follow these steps:

### Step 1: Substitute \( \sin x \) with \( t \)
Let \( t = \sin x \). The inequality becomes:
\[ 4t^2 - 8t + 3 \leq 0 \]
We need to find the values of \( t \) that satisfy this inequality.
...