Solve the equation for x: `cos^2[pi/4(sinx+sqrt(2)cos^2x)]-tan^2[x+pi/4tan^2x]=1`

Explanation

To solve the equation

\[ \cos^2\left(\frac{\pi}{4}\right)\left(\sin x + \sqrt{2}\cos^2 x\right) - \tan^2\left(x + \frac{\pi}{4}\tan^2 x\right) = 1, \]

we will follow these steps:

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