Two uniform solid spheres of equal radii are so placed that one is directly above the other. The bottom sphere is fixed, and the top sphere, initially at rest, rolls off. At what point will contact between the two spheres be "lost"? Assume the coefficient of friction is such that no slipping occurs. The original answer is in the format \theta=\arccos (m / n), please give the value of m + n.

Let's think step by step and output the final answer within \boxed{}.
user