# 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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