The complete interval of values of $x$ in $\left(-\frac{\pi }{2}, \frac{\pi }{2}\right)$ satisfying the inequality $\cos x·\cos 2x>-\frac{1}{4}$ and $3\cos x>1,$ is

Let $f:\left[0, 2\right]\to ℝ$ be the function defined by

$f\left(x\right)=\left(3-\sin \left(2\pi x\right)\right)\sin \left(\pi x-\frac{\pi }{4}\right)-\sin \left(3\pi x+\frac{\pi }{4}\right)$.

If $\alpha , \beta \in \left[0, 2\right]$ are such that $\left\{x\in \left[0, 2\right] :f\left(x\right)\ge 0\right\}=\left[\alpha , \beta \right]$, then the value of $\beta -\alpha$ is _____

Find $\theta \in \left[\frac{\pi }{2},\frac{3\pi }{2}\right]$ satisfying $2{\cos }^2\theta +\sin \theta \le 2$.

If  $A=\left\{\theta :2{\cos }^2\theta +\sin \theta \le 2\right\} \& B=\left\{\theta :\frac{\pi }{2}\le \theta \le \frac{3\pi }{2}\right\}$and . Then, $A\cap B$ is equal to