The number of ordered pairs (x, y) of real numbers satisfying $4{\mathrm{x}}^2-4\mathrm{x}+2={\sin }^2\mathrm{y}\text{ and }{\mathrm{x}}^2+{\mathrm{y}}^2\le 3$ is equal to ______

The given equation can be rewritten as
(2x-1)²+1=sin²y, which is possible only when $\mathrm{x}=\frac{1}{2}$
${\sin }^2\mathrm{y}=1\Rightarrow \mathrm{y}=\frac{-\mathrm{\pi }}{2},\frac{\mathrm{\pi }}{2}\left[\mathrm{as}{\mathrm{x}}^2+{\mathrm{y}}^2\le 3\right]$
Thus, there are only two pairs (x, y) satisfying the
given equation. They are $$$\left(\frac{1}{2},\frac{-\mathrm{\pi }}{2}\right) \mathrm{and} \left(\frac{1}{2},\frac{-\mathrm{\pi }}{2}\right)$