# A NT Problem in Disguise

Geometry Level 5

Find the smallest natural number $$a$$ for which the equation

$\cos^2(\pi(a-x))-2\cos(\pi(a-x))+\cos\left(\dfrac{3\pi x}{2a}\right)\cos\left(\dfrac{\pi x}{2a}+\dfrac{\pi}{3}\right)+2=0$

has a real root.

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