Find the values of x in the interval `[0,2pi]` which satisfy the inequality:
`3|2sinx-1|ge3+4cos^(2)x`

Explanation

To solve the inequality \( 3|2\sin x - 1| \geq 3 + 4\cos^2 x \) for \( x \) in the interval \( [0, 2\pi] \), we can follow these steps:

### Step 1: Rewrite the Inequality
We start with the given inequality:
\[ 3|2\sin x - 1| \geq 3 + 4\cos^2 x \]
We can express \( \cos^2 x \) in terms of \( \sin x \) using the identity \( \cos^2 x = 1 - \sin^2 x \):
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