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. Start with the equation:
\[ 2\sin^2 x + \sin^2 2x = 2 \]
...