Midpoint Locus Circle Radius Angle

The locus of the mid points of the chords of the circle C1:(x−4)2+(y−5)2=4 which subtend an angle θi at the centre of the circle C1, is a circle of radius ri. If θ1=‌

π

3

,θ3=‌

2π

3

and r12=r22+r32, then θ2 is equal to