Minimize The Expression 7

Geometry Level 4

\[ \left(\dfrac{\cos A}{\cos B} \right)^2+ \left(\dfrac{\cos B}{\cos C} \right)^2+\left(\dfrac{\cos C}{\cos A} \right)^2+8\cos A \cos B \cos C\]

If \(A, B, C\) are the angles of an acute angled triangle, minimize the expression above.

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