The Ladder from the IPhOO

A uniform ladder of mass \( m \) and length \( \mathcal{L} \) is resting on a wall. A man of mass \( m \) climbs up the ladder and is in perfect equilibrium with the ladder when he is \( \frac{2}{3}\mathcal{L} \) the way up the ladder. The ladder makes an angle of \( \theta = 30^\circ \) 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 \( \mu \), what is \( 1000 \cdot \mu \), expressed to the nearest integer?

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