The number of solutions of the pair of equations `2sin^2 theta - cos(2 theta)=0,2cos^2 theta-3sin theta=0` in the interval `[0,2pi]` is

Explanation

To find the number of solutions of the pair of equations

1. \( 2\sin^2 \theta - \cos(2\theta) = 0 \)
2. \( 2\cos^2 \theta - 3\sin \theta = 0 \)

in the interval \([0, 2\pi]\), we will solve each equation step by step.

### Step 1: Solve the first equation
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