Traumatizing Trigonometry

Geometry Level pending

What is the maximum value of \(x\) which satisfies the equation \({ 8 }^{ \left( 1+\left| \cos { x } \right| +\left| \cos ^{ 2 }{ x } \right| +\left| \cos ^{ 3 }{ x } \right| +\left| \cos ^{ 4 }{ x } \right| +............. \right) }={ 4 }^{ 3 }\) in the range of \(\left( -180^\circ ,180^\circ \right)\).

\(Note:\)

Enter your answer in degree.

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