To find the value of x, we first solve the equation \(4\sin^2 x - 3 = 0\) for sin^2x:

\(4\sin^2 x = 3\).

Now, solve for sin x:

\(\sin^2 x = \frac{3}{4}\).

Take the square root of both sides:

\(\sin x = \sqrt{\frac{3}{4}}\).

\(\sin x = \frac{\sqrt{3}}{2}\).

Now, find the angle whose sine is \(\frac{\sqrt{3}}{2}\). This is a standard angle, and we know that \(\sin 60° = \frac{\sqrt{3}}{2}\).

So, \(x = 60°\)