If the line $3 x - 2 y + 12 = 0$ intersects the parabola $4 y = 3 x ^ { 2 }$ at the points $A$ and $B$, then at the vertex of the parabola, the line segment $A B$ subtends an angle equal to
(1) $\tan ^ { - 1 } \left( \frac { 4 } { 5 } \right)$
(2) $\tan ^ { - 1 } \left( \frac { 9 } { 7 } \right)$
(3) $\tan ^ { - 1 } \left( \frac { 11 } { 9 } \right)$
(4) $\frac { \pi } { 2 } - \tan ^ { - 1 } \left( \frac { 3 } { 2 } \right)$