$\frac{1}{\sin(\theta)}=\frac{2\sqrt{3}}{3}$

$\sin(\theta)=\frac{3}{2\sqrt{3}}$

$\sin(\theta)=\frac{3}{2\sqrt3}\left(\frac{\sqrt3}{\sqrt3}\right)$

$\sin(\theta)=\frac{\sqrt3}{2}$

$\frac{1}{\cos(\theta)}=-\frac{\sqrt{2}}{1}$

$\frac{\sin(\theta)}{\cos(\theta)}=\frac{1}{0}$

$\frac{\cos(\theta)}{\sin(\theta)}=-1$