<s>[INST] What is the minimum value of $(\tan^2)(A/2)+(\tan^2)(B/2)+(\tan^2)(C/2)$, where $A$, $B$ and $C$ are angles of a triangle 
What is the minimum value of $(\tan^2)(A/2)+(\tan^2)(B/2)+(\tan^2)(C/2)$, where $A$, $B$ and $C$ are angles of a triangle?

I know that the sum of the angles is $\pi$, but I am unable to find the minimum value of the above expression.
 [/INST] Just another way:  noting $\tan^2 \frac x 2$ is convex, by Jensen's inequality you have
$$\tan^2\frac A 2 + \tan^2 \frac B 2 + \tan^2 \frac C 2 \ge 3\tan^2\frac{A+B+C}{2\cdot 3 } = 1$$
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