You can use the trigonometric identity [tex]1+\cot^2{x}=\csc^2{x}[/tex].
[tex]1+\cot^2{\theta}=(\frac{-\sqrt{37}}{6} )^2 \\ 1+\cot^2{\theta}=\frac{37}{36} \\ \cot^2{\theta}=\frac{1}{36} \\
\cot{\theta}=\frac{1}{6}[/tex]
The requirement that [tex]\tan{\theta}\ \textgreater \ 0[/tex] eliminates -1/6 from being another solution.
