Prove that in any triangle ABC:

$\sqrt{(\tan \frac{A}{2} + \tan \frac{B}{2})(\tan \frac{B}{2}+\tan \frac{C}{2})} + \sqrt{(\tan \frac{B}{2} + \tan \frac{C}{2})(\tan \frac{C}{2}+\tan \frac{A}{2})}+ \sqrt{(\tan \frac{C}{2} + \tan \frac{A}{2})(\tan \frac{A}{2}+\tan \frac{B}{2})} \leq 2(\cot A + \cot B + \cot C)$