Solve the following equation: `sintheta+sin5theta=sin3theta`

Explanation

`sintheta+sin5theta=sin3theta,0≤theta≤π`

`sintheta+sin5theta=sin3theta`

⇒`2sin((theta+5theta​)/2)cos((theta−5theta​)/2)=sin3theta`

⇒`2sin3thetacos2theta=sin3theta`

⇒`sin3theta(2cos2theta−1)=0`

⇒`sin3theta=0` or `2cos2theta−1=0`

⇒`3theta=nπ(n∈0,1,........)` or `costheta=1/2`

⇒`theta=nπ/3`

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