There is a second derivative test for functions of two variables. We'll use the notation "Rtt" to stand for the second partial derivative of R with respect to theta twice. Let A = Rtt, B = Rtp, C = Rpp at a point where both first partial derivatives are zero. If B^2 - AC > 0, then you have a saddle point (neither a minimum or a maximum). If B^2 - AC < 0 and A>0, then you have a local minimum. If B^2 - AC < 0 and A<0, then you have a local maximum. Use this test to locate the angles at which some local minima of the total repulsive force occur.