Solve the equation:
$\displaystyle \frac{1}{1+\sqrt{2} \sin x}+\frac{1}{1+ \sqrt{2} \cos x}=(\sqrt{2})^{1+x} , \, x \in \left( -\frac{\pi}{4}, \frac{\pi}{4} \right).$
Equation
For discussing Olympiad Level Algebra (and Inequality) problems
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