The line $y = x + 1$ intersects the ellipse $\frac { x ^ { 2 } } { 2 } + \frac { y ^ { 2 } } { 1 } = 1$ at $A$ and $B$. Find the angle sub-stained by segment AB and centre of ellipse is\
(A) $\frac { \pi } { 2 } + \tan ^ { - 1 } \left( \frac { 1 } { 2 } \right)$\
(B) $\frac { \pi } { 2 } + 2 \tan ^ { - 1 } \left( \frac { 1 } { 4 } \right)$\
(C) $\frac { \pi } { 2 } + \tan ^ { - 1 } \left( \frac { 1 } { 4 } \right)$\
(D) $\frac { \pi } { 2 } - \tan ^ { - 1 } \left( \frac { 1 } { 4 } \right)$