A pair of wedges are located on a horizontal surface. The coefficient of friction (both sliding and static) between the wedges is \mu, the coefficient of friction between the bottom wedge \mathrm{B} and the horizontal surface is \mu, and the angle of the wedge is \theta. The mass of the top wedge \mathrm{A} is m, and the mass of the bottom wedge \mathrm{B} is M=2 \mathrm{~m}. A horizontal force F directed to the left is applied to the bottom wedge as shown in the figure.

Determine the range of values for F so that the the top wedge does not slip on the bottom wedge. Express your answer(s) in terms of any or all of m, g, \theta, and \mu.