Hi,[tex] \dfrac{2}{3} =cotg\ \theta =\dfrac{cos\ \theta}{sin\ \theta}\\\\
\Rightarrow\ 2*sin\ \theta=3*cos\ \theta\\\\
\Rightarrow\ 2*sin\ \theta=3* \sqrt{1-sin^2\ \theta} \\\\
\Rightarrow\ 4*sin^2\ \theta=9* (1-sin^2\ \theta}) \\\\
\Rightarrow\ 13*sin^2\ \theta=9) \\\\
\Rightarrow\ sin\ \theta= \dfrac{3}{ \sqrt{13} } \\\\
\Rightarrow\ \dfrac{1}{sin\ \theta}=cosec\ \theta= \dfrac{ \sqrt{13} }{3} \\\\
\boxed{cosec\ \theta= \dfrac{ \sqrt{13} }{3} }[/tex]
Maybe "cosec a, cotg a" (in french) is written "csc a,cot a" in american
