case 1, R^{2}=(3P)^{2}+(2P)^{2}+2*3*2*P^{2}*cosΘ = 9P^{2}+4P^{2}+12P^{2}cosΘ = 13P^{2}+12P^{2}cosΘ ----->(1)
case 2, (2R)^{2}=(6P)^{2}+(2P)^{2}+2*6*2*P^{2}*cosΘ ; 4R^{2}=36P^{2}+4P^{2}+24P^{2}cosΘ = 40P^{2}+24P^{2}cosΘ ------->(2)
Multiply (1) by 4; 4R^{2}=52P^{2}+48P^{2}cosΘ ------>(3)
(3)-(2) gives, 0=12P^{2}+24P^{2}cosΘ
Therefore, cosΘ = (-1/2) => Θ = cos^{-1}(-1/2) = 120°