# Trigonometry! #66

Geometry Level 4

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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