Answer
$\sqrt {15}$
Work Step by Step
The trigonometric ratios are as follows: $\sin \theta= \dfrac{opposite}{hypotenuse}$ ; $\cos \theta= \dfrac{Adjacent}{hypotenuse}$ and $\tan \theta= \dfrac{Opposite}{Adjacent}$
Since,
$\cot \theta=\tan (90^{\circ}-\theta)$
So, $\cot \theta=\dfrac{\cos \theta}{\sin \theta}=\dfrac{\sqrt {15}/4}{1/4}$
Our required answer is: $\tan (90^{\circ}-\theta)=\sqrt {15}$
