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Find the general value of theta from the...

Find the general value of `theta` from the equation `sinalpha+sin(alpha+theta)+sin(alpha+2theta)=0`.

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`sinalpha+sin(alpha+theta)+sin(alpha+2theta)=0`
`rArr sin(alpha+2theta)+sinalpha+sin(alpha+theta)=0`
`rArr 2sin(alpha+theta).costheta+sin(alpha+theta)=0`
`rArr sin(alpha+thetaA)(2costheta+1)=0`
`rArr sin(alpha+theta)=0` or `2costheta+1=0`
Now `sin(alpha+theta)=0`
`rArr alpha+theta=npi`
and `2costheta+1=0`
`rArr costheta=-1/2=-cospi/3`
`=cos(pi-pi/3)=cos(2pi)/(3)`
`rArr theta+-(2pi)/(3)`. Ans.
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