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 θ_i at the centre of the circle C_1, is a circle…

The locus of the mid points of the chords of the circle $\displaystyle C_1:(x-4)^2+(y-5)^2=4$ which subtend an angle $\displaystyle \theta_i$ at the centre of the circle $\displaystyle C_1$, is a circle of radius $\displaystyle r_i$. If $\displaystyle \theta_1=\frac{\pi}{3}, \theta_3=\frac{2 \pi}{3}$ and $\displaystyle r_1^2=r_2^2+r_3^2$, then $\displaystyle \theta_2$ is equal to