Two parallel chords of a circle of radius 2 are at a distance $\sqrt { 3 } + 1$ apart. If the chords subtend at the center, angles of $\frac { \pi } { k }$ and $\frac { 2 \pi } { k }$, where $k > 0$, then the value of $[ k ]$ is\\
[Note : [k] denotes the largest integer less than or equal to k]