One Equation, One Variable!

Geometry Level 5

\[\large{ x \left ( \ \sqrt{3 - 2x + \sqrt{5(1-x^2)}} + \sqrt{\dfrac{3}{2}}\ \right) = \sqrt{\dfrac{2}{3}} } \]


If \(\large{x = \cos \left( \dfrac{A\pi^B + \arccos (C/D) }{E} \right) }\) such that it satisfies the above equation, where \(A,B,C,D,E\) are positive integers, find the minimum value of \(A+B+C+D+E\).

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