The Ladder from the IPhOO

A uniform ladder of mass m m and length L \mathcal{L} is resting on a wall. A man of mass m m climbs up the ladder and is in perfect equilibrium with the ladder when he is 23L \frac{2}{3}\mathcal{L} the way up the ladder. The ladder makes an angle of θ=30 \theta = 30^\circ with the horizontal floor. If the coefficient of static friction between the ladder and the wall is the same as that between the ladder and the floor, which is μ \mu , what is 1000μ 1000 \cdot \mu , expressed to the nearest integer?

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