The block will move if

$F \cos \theta \geq f_{\max }$

$F \cos \theta \geq \mu(W-F \sin \theta)$

$\mu=\tan \alpha=\frac{\sin \alpha}{\cos \alpha}$

$F \cos \theta \geq \frac{\sin \alpha}{\cos \alpha}(W-F \sin \theta)$

$F(\cos \theta \cos \alpha+\sin \theta \sin \alpha) \geq W \sin \alpha$

$F \geq \frac{W \sin \alpha}{\cos (\theta-\alpha)}$

$F_{\min }=\frac{W \sin \alpha}{\cos (\theta-\alpha)}$