Mystery polynomial equation in 2019.

Algebra Level 5

If the number cc is the largest solution of the equation (xcosπ2020)(xcos3π2020)(xcos5π2020)(xcos2019π2020)=121010, \left(x-\cos {\frac{\pi}{2020}}\right) \left(x-\cos {\frac{3\pi}{2020}}\right) \left (x-\cos {\frac{5\pi}{2020}} \right )\cdots \left( x-\cos {\frac{2019\pi}{2020}}\right) =\frac{1}{2^{1010}}, then find the number 1arccosc.\left \lfloor{\frac{1}{\arccos{c}}}\right\rfloor.

Note: The expression 1arccosc\left \lfloor{\frac{1}{\arccos{c}}}\right\rfloor represents the floor of the number 1arccosc.\frac{1}{\arccos{c}}.

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