A smooth hemisphere of radius 1.6a is placed plane face down and fixed onto a horizontal plane. A particle r of mass 2m is placed on the top of the hemisphere and projected with speed √1/4ga. As the particle travels 4 down the curved surface of the hemisphere it turns through an angle θ, where θ is measured from the vertical through the centre of the hemisphere. Find the value of θ when the particle loses contact with the hemisphere.