Find all integral solutions to $a+b+c=abc$. Find all integral solutions of the equation $a+b+c=abc$.  
Is $\{a,b,c\}=\{1,2,3\}$ the only solution? I've tried by taking $a,b,c=1,2,3$.

If you are looking for a general solution (not necessarily restricted to integers), here is one $(\tan \theta_1, \tan \theta_2, \tan \theta_3)$ where $\theta_1+\theta_2+\theta_3=\pi$.
