The locus of the middle 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 $$C_i$$, is a circle of radius $$r_i$$. If $$\theta_1 = \frac{\pi}{3}$$, $$\theta_3 = \frac{2\pi}{3}$$ and $$r_1^2 = r_2^2 + r_3^2$$, then $$\theta_2$$ is equal to

A

$$\frac{\pi}{4}$$

B

$$\frac{3\pi}{4}$$

C

$$\frac{\pi}{6}$$

D

$$\frac{\pi}{2}$$