Three Variables-Inequality with $a+b+c=abc$ $a$,$b$,$c$ are positive numbers such that $~a+b+c=abc$
Find the maximum value of $~\dfrac{1}{\sqrt{1+a^{2}}}+\dfrac{1}{\sqrt{1+b^{2}}}+\dfrac{1}{\sqrt{1+c^{2}}}$

HINT:
Put $a=\tan A$ etc. so that $A+B+C=n\pi$ 
Now $\frac1{\sqrt{1+a^2}}=\cos A$
Use this
