Finding angle X when given an inequation and a weird equation

[Paulo Serrano]

Homework Statement

sin (x) + sin (2x) + sin (3x) = 0
http://www4b.wolframalpha.com/Calculate/MSP/MSP531196eg6ff0edb8i9400000gb08c7ag3hfbfeh?MSPStoreType=image/gif&s=8

Sorry for not following the recommended layout, it's just that this question boggles me and I don't know any relevant formulas or where to start.

I know the http://www28.wolframalpha.com/input/?i=sin+x+++sin+2x+++sin+3x+=+0,+pi/2+<+x+<+pi"but I don't know how to get to it.

Thanks in advance to whoever tries to help

 

[rock.freak667]

Do you know a formula for sinP+sinQ? (or the sum to product formula for sin?)

 

[Mentallic]

Use the double-angle formula to expand the $$sin(2x)$$ and $$sin(3x)$$ - notice that $$sin(3x)=sin(2x+x)$$ , then collect like terms and factor as much as possible while using $$sin^2(x)+cos^2(x)=1$$ to aid you in the factoring process.