Find common roots of the equations `2sin^2x+sin^2 2x=2a n dsin2x+cos2x=tanxdot`

Explanation

To find the common roots of the equations \(2\sin^2 x + \sin^2 2x = 2\) and \(\sin 2x + \cos 2x = \tan x\), we will solve each equation step by step and then find the common solutions.

### Step 1: Solve the first equation \(2\sin^2 x + \sin^2 2x = 2\)

1. **Rewrite \(\sin^2 2x\)**:
\[ \sin^2 2x = (2\sin x \cos x)^2 = 4\sin^2 x \cos^2 x \]
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