Find the real root for this equation

Geometry Level pending

\[\large{{{\left( \sqrt[4]{17-12\sqrt{2}} \right)}^{\sqrt{\sin 2x}+\frac{1}{\sqrt{\sin 2x}}}}+{{\left( \sqrt[4]{17+12\sqrt{2}} \right)}^{\sqrt{\sin 2x}+\frac{1}{\sqrt{\sin 2x}}}}=6}\]

Find real number \(x\) satisfying the equation above.

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