Answer
$\\cot\theta$ = - $\frac{\sqrt 5}{2}$
Work Step by Step
To find $\cot\theta$, we will calculate $\cos\theta$ first-
We know from first Pythagorean identity that-
$\cos\theta$ = ± $\sqrt (1-\sin^{2}\theta)$
As $\theta$ terminates in Q II, Therefore $\cos\theta$ will be negative-
$\cos\theta$ = - $\sqrt (1-\sin^{2}\theta)$
substitute the given value of $\sin\theta$-
$\cos\theta$ = - $\sqrt (1-(\frac{2}{3})^{2})$
$\cos\theta$ = - $\sqrt (1-\frac{4}{9})$
$\cos\theta$ = - $\sqrt (\frac{9 - 4}{9})$ = $\sqrt (\frac{5}{9})$
$\cos\theta$ = - $\frac{\sqrt 5}{3}$
By ratio identity-
$\cot\theta$ = $\frac{\cos\theta}{\sin\theta}$
Substituting the values of $\cos\theta$ and $\sin\theta$-
$\\cot\theta$ = $\frac{-\sqrt 5/3}{2/3}$ = - $\frac{\sqrt 5}{2}$
