Question 3
Given a triangle $ABC$, find the minimum of
$$S=\frac{\cos^2(A/2)\cos^2(B/2)}{\cos^2(C/2)}+\frac{\cos^2(B/2)\cos^2(C/2)}{\cos^2(A/2)}+\frac{\cos^2(C/2)\cos^2(A/2)}{\cos^2(B/2)}.$$
$$S=\frac{\cos^2(A/2)\cos^2(B/2)}{\cos^2(C/2)}+\frac{\cos^2(B/2)\cos^2(C/2)}{\cos^2(A/2)}+\frac{\cos^2(C/2)\cos^2(A/2)}{\cos^2(B/2)}.$$