Find the values of \(x\) in \((-\pi,\pi)\) which satisfy the equation. \[8^{(1+\lvert\cos x\rvert+\cos^{2}x+\lvert\cos^{3}x\rvert+...)}=64\]

Express the four values of \(x\) in the form of \(±\frac {a\pi}{b}\) and \(±\frac {c\pi}{d}\) such that \(a,b,c\) and \(d\) are integers and where \(gcd(a,b)=gcd(c,d)=1\). Enter the value of \(a+b+c+d\).

This problem is part of the set Trigonometry.

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