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 $$A+B+C+D+E$$.

×