# Give your problem a cool name (Optional)

Geometry Level 5

Let $$ABC$$ be an acute angled triangle. Let $$A,B,C$$ be its angles. For $$n=1,2,3$$ , we define

$\large x_{n}=2^{n-3} \left(\displaystyle\sum_{cyc \{A,B,C\}}\cos^n A \right) + \prod_{cyc\{A,B,C\}} cos A$

Find the minimum value of $$\large\displaystyle\sum_{n=1}^{3} x_n$$

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