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
(1) $\frac { \pi } { 4 }$
(2) $\frac { 3 \pi } { 4 }$
(3) $\frac { \pi } { 6 }$
(4) $\frac { \pi } { 2 }$