The minimum value of $‘F’$ so that block is in equilibrium is
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$\Sigma F_{y}=0$
$\mathrm{N} \cos 60^{\circ}+\mathrm{f}_{\mathrm{max}} \sin 60^{\circ}+\mathrm{F} \sin \theta-\mathrm{Mg}=0 \ldots(\mathrm{i})$
$\Sigma F_{x}=0$
$\mathrm{f}_{\mathrm{max}} \cos 60^{\circ}+\mathrm{F} \cos \theta-\mathrm{N} \sin 60^{\circ}=0$ $...(ii)$
$f_{\max }=\mu N$ $...(iii)$
$\frac{\mathrm{d} \mathrm{F}}{\mathrm{d} \theta}=0$ $...(iv)$
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