text: I wish there was some way to include a drawing in the answers.\nStarting from the end, we want the bob to complete a vertical circle about the peg. The radius of this circle will be L/3. The minimum velocity to complete the circle is given by\nv = sqrt (5*g*r) = sqrt (5*g*L/3).\nHence the KE of the bob at the lowest point is\nKE = 1/2 m*v^2 = 5/6 m*g*L. \nThis must be equal to the PE at the beginning of the swing.\nPE = m*g*L*(1 - cos theta).\nThis gives cos theta = 1 - 5/6 = 1/6. Thus the required angle = arccos 1/6 = 80.4 deg. \nFor the derivation of the min velocity for completion of a vertical circle, pl refer to any standard text book on Mechanics.