Problem no. 18

Geometry Level pending

\[ \frac{1}{\sin({\frac{x}{2^{2015}}})}=2^{2015}\sqrt{2}\cos({\frac{x}{2}})\cos({\frac{x}{4}})\ldots \cos({\frac{x}{2^{2015}}})\]

Determine the value of \(x\), where \(0\leq x\leq\frac{\pi}{2}\) which satisfies the equation above.

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