If `asintheta="bsin"(theta+(2pi)/3)="csin"(theta+(2pi)/3)` , prove that `a b+b c+c a=0.`

If asintheta="bsin"(theta+(2pi)/3)="csin"(theta+(4pi)/3) , prove that a b+b c+c a=0.

If a sin theta=bsin(theta+(2 pi)/(3))=csin(theta+(2 pi)/(3)) prove that ab+bc+ca=0

If asintheta=bsin(theta+(2pi)/(3))=csin(theta+(4pi)/(3)) then prove that, ab+bc+ca=0 .

If a cos theta = b cos ( theta+(2 pi)/3)= c cos ( theta+ (4pi)/3),"prove that" ab+bc+ca=0.

If asintheta = bsin(theta+(2pi)/(3)) = csin(theta+(4pi)/(3)) , then the value of ab+bc+ca is ___________.

Prove that sintheta+sin(theta+(2pi)/(3))+sin(theta+(4pi)/(3))=0

Prove that: 4sin theta sin(theta+(pi)/(3))sin(theta+(2 pi)/(3))=sin3 theta

If sin^(3)theta+sin^(3)(theta+(2pi)/(3))+sin^(3)(theta+(4pi)/(3))=a sinb theta . Find the value of |(b)/(a)| .

If sin^(3)theta+sin^(3)(theta+(2pi)/(3))+sin^(3)(theta+(4pi)/(3))=a sinb theta . Find the value of |(b)/(a)| .

Prove that "sin"((2pi)/3+theta)-"sin"((2pi)/3-theta) + sintheta=0