Let θ∈0,4π satisfy the equation sinθ+2sinθ+3sinθ+4=6 .If the sum of all the values of θ is of the form kπ , then the value of k is

# Let $\theta \in \left[0,4\pi \right]$ satisfy the equation $\left(\mathrm{sin}\theta +2\right)\left(\mathrm{sin}\theta +3\right)\left(\mathrm{sin}\theta +4\right)=6$ .If the sum of all the values of $\theta$ is of the form $k\pi$ , then the value of k is

1. A

6

2. B

5

3. C

4

4. D

2

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