Mopping baby

In the above figure, a baby pushes directly along the handle of a mop with a force of \( F. \) The handle is at an angle of \( \theta\) with the vertical, and \( \mu_s = \frac{1}{\sqrt{3}} \) and \( \mu_k = \frac{1}{3} \) are the coefficients of static and kinetic frictions, respectively, between the head of the mop and the floor. If the mop has no mass and \( \theta \) is less than some angle \( \theta_0, \) then the baby is unable to move the head of the mop. What is \( \theta_0 \) in degrees?

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