The locus of the mid points of the chords of the circle ${C_1}:{(x - 4)^2} + {(y - 5)^2} = 4$ which subtend an angle ${\theta _i}$ at the centre of the circle $C_1$, is a circle of radius $r_i$. If ${\theta _1} = {\pi \over 3},{\theta _3} = {{2\pi } \over 3}$ and $r_1^2 = r_2^2 + r_3^2$, then ${\theta _2}$ is equal to :