If `sintheta+sinphi=sqrt3(cosphi-costheta))` , prove that `sin3theta+sin3phi=0`

Explanation

Given,

`sintheta+sinphi=√3(cosphi−costheta)`

using `sinA+sinB=sin((A+B)/2)cos((A-B)/2)` and `cosA+cosB=sin((A+B)/2)sin((A-B)/2)`

`=>sin(theta+phi)/2cos(theta-phi)/2=sqrt(3)sin(theta+phi)/2sin(theta-phi)/2`

`tan(theta-phi)/2=sqrt3`

or,

`=>theta+phi=2npi`

Given,

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