I need help on the following problem.
Let $x,y,z$ be the positive real numbers and satisfy $x+y+z=xyz$
then,
$\frac{x}{\sqrt{1+x^{2}}}+\frac{y}{\sqrt{1+y^{2}}}+\frac{z}{\sqrt{1+z^{2}}}\leq\frac{3\sqrt{3}}{2}$
I tried with $x=tan\alpha,y=tan\beta,z=tan\gamma$ and LHS reduses to
$sin\alpha+sin\beta+sin\gamma$ but I don't know how to utilize $x+y+z=xyz$
Any help is appreciated, thanks.
