Let `theta in [0,4pi]` satisfy the equation `(sintheta+2)(sintheta+3)(sintheta+4)=6.` If the sum of all the values of `theta` is of the form `kpi` , then the value of `k` is 6 (b) 5 (c) 4 (d) 2

Explanation

To solve the equation \((\sin \theta + 2)(\sin \theta + 3)(\sin \theta + 4) = 6\) for \(\theta\) in the interval \([0, 4\pi]\), we can follow these steps:

### Step 1: Analyze the equation
We start with the equation:
\[ (\sin \theta + 2)(\sin \theta + 3)(\sin \theta + 4) = 6 \]
Let \(x = \sin \theta\). Then the equation becomes:
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