\(\sin^2a+\cos^2a=1\Leftrightarrow\sin^2a=1-\dfrac{9}{16}=\dfrac{7}{16}\\ \Leftrightarrow\sin a=\dfrac{\sqrt{7}}{4}\Leftrightarrow\tan a=\dfrac{\sin a}{\cos a}=\dfrac{\sqrt{7}}{4}:\dfrac{3}{4}=\dfrac{\sqrt{7}}{3}\\ \Leftrightarrow\cot a=\dfrac{3}{\sqrt{7}}=\dfrac{3\sqrt{7}}{7}\)