Solve the equation `(sinx+cosx)^(1+sin2x)=2`, when `0 lexlepi`

Explanation

To solve the equation \((\sin x + \cos x)^{(1 + \sin 2x)} = 2\) for \(0 \leq x \leq \pi\), we can follow these steps:

### Step 1: Analyze the equation
We know that the expression \(\sin x + \cos x\) can be maximized. The maximum value of \(\sin x + \cos x\) is \(\sqrt{2}\), which occurs at \(x = \frac{\pi}{4}\).