Given that $0 < x < \frac { \pi } { 2 }$ and $\cot \mathrm { x } - 3 \tan \mathrm { x } = \frac { 1 } { \sin 2 \mathrm { x } }$, what is $\sin ^ { 2 } x$?\\ A) $\frac { 1 } { 9 }$\\ B) $\frac { 1 } { 8 }$\\ C) $\frac { 1 } { 7 }$