If \( 1+2 \sin x+3 \sin ^{2} x+4 \sin ^{3} x+\ldots \) upto infinite terms \( =4 \) and number o...

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If \( 1+2 \sin x+3 \sin ^{2} x+4 \sin ^{3} x+\ldots \) upto infinite terms \( =4 \) and number of solutions of the equation in \( \left[\frac{-3 \pi}{2}, 4 \pi\right] \) is \( k \). The value of \( k \) is equal to
(a) 4
(b) 5
(c) 6
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