10. By first showing that \(\frac { 16 + 9 \sin ^ { 2 } \theta } { 5 - 3 \cos \theta }\) can be expressed in the form \(p + q \cos \theta\), where \(p\) and \(q\) are integers, find the least possible value of \(\frac { 16 + 9 \sin ^ { 2 } \theta } { 5 - 3 \cos \theta }\). State the exact value of \(\theta\), in radians in the interval \(0 \leqslant \theta < 2 \pi\), at which this least value occurs.