$\begin{align}  & \cot \left( t-\frac{\pi }{3} \right)=\frac{1}{\tan (t-\tfrac{\pi }{3})}=\frac{1}{\tfrac{\tan t-\tan \tfrac{\pi }{3}}{1+\tan t\tan \tfrac{\pi }{3}}} \\ & \text{Note:}\frac{\pi }{3}radian={{60}^{\circ }} \\ & \cot \left( t-\frac{\pi }{3} \right)=\frac{1+\tan t\tan \tfrac{\pi }{3}}{\tan t-\tan \tfrac{\pi }{3}} \\ & \cot \left( t-\frac{\pi }{3} \right)=\frac{1+\sqrt{3}\tan t}{\tan t-\sqrt{3}} \\\end{align}$