Find the number of solution of `[cosx]+|sinx=1inpilt=xlt=3pi` where `[ `` ]` denotes the greatest integer function.

Explanation

To solve the equation \([ \cos x ] + | \sin x | = 1\) for \(x\) in the interval \([\pi, 3\pi]\), we will analyze the possible values of \([ \cos x ]\) and \(| \sin x |\).

### Step 1: Determine the range of \(\cos x\) and \(\sin x\)

The cosine function, \(\cos x\), oscillates between -1 and 1 for all \(x\). Therefore, the greatest integer function \([ \cos x ]\) can take the values:
- \(-1\) when \(-1 < \cos x < 0\)
- \(0\) when \(0 \leq \cos x < 1\)
- \(1\) when \(\cos x = 1\)
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