If $A+B+C=180^\circ, \cot A=2$ and $\cot B= \frac34$, what is $\sin C$? 
If $A+B+C=180^\circ, \cot A=2$ and $\cot B= \frac34$, what is $\sin C$?

$$\cot A = 2\\
\frac{\cos A }{ \sin A }= 2\\
\cot B = \frac34\\
\frac{\cos B }{ \sin B} = \frac34$$
What should I do with $A+B+C=180^\circ$?

$\tan C = -\tan (A+B)= \dfrac{\tan A+\tan B}{\tan A\tan B- 1}=...=-\dfrac{11}{2}\implies \cot C = -\dfrac{2}{11}\implies \cot^2C= \dfrac{4}{121}\implies \csc^2C= 1+\cot^2C= \dfrac{125}{121}\implies \sin^2C = \dfrac{121}{125}\implies \sin C = \dfrac{11}{5\sqrt{5}}$ . 
