For the case where angle \(B A C = \frac { 1 } { 6 } \pi\) radians, find \(k\) correct to 4 significant figures.
For the general case in which angle \(B A C = \theta\) radians, where \(0 < \theta < \frac { 1 } { 2 } \pi\), it is given that \(\frac { \theta } { \sin \theta } > 1\). Find the set of possible values of \(k\).