How can i solve this equation? Sin sin^(3)x + 3sin {}^(2) x + 2 \sin x = 0 Please help me if you can

Question

How can i solve this equation?

Sin

`sin^(3)x + 3sin {}^(2) x + 2 \sin x = 0`
Please help me if you can

Answer 1

Factorizing sin2x+3sinx+2=0

sin^2 x+2sinx+sinx+2=0

or sinx(sinx+2)+1(sinx+2)=0

or (sinx+1)(sinx+2)=0

Now as sinx+2≠0, we have sinx+1=0

or sinx= −1 =sin(3π/2)

Hence, x=2nπ+3π/2