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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