Domainomania

Geometry Level 4

\[ \large f(x)=\sqrt {\log_x \cos(2\pi x)}\]

If the domain of \( f(x) \) can be represented as \(\left(a,\dfrac {y}{z} \right)\cup \left (\dfrac{b}{c},d \right )\cup\{e,f,g, \ldots\} \), where \(y\) and \(z\), and \(b\) and \(c\) are coprime integers, find the value of \(a+y+z+b+c+d\).

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