An object with weight $W$ is dragged along a horizontal plane whose $\mu=1.5$ (coefficient of friction) by a force acting along a rope attached to the object. If the rope makes an angle $\theta$ with the plane, then the magnitude of the force is:

$F=\dfrac{\mu W}{\mu\sin \theta + \cos \theta}$

where $0\leq \theta \leq \dfrac{\pi}{2}$ .If there exists a value $\alpha$ for $\theta$ such that $F$ is minimized, find the value of $\tan \alpha$ .

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