Leaving the Hemisphere

A point particle of mass m sits at rest on top of a frictionless hemisphere of mass M, which rests on a frictionless table, as shown. The particle is given a tiny kick and slides down the hemisphere. At what angle $\theta$ (measured from the top of the hemisphere, and measured in degrees) does the particle lose contact with the hemisphere if the ratio of $M$ to $m$ is 2?

Clarification: $m \ne M$ .

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