If `x\ costheta=y cos(theta+(2pi)/3)=z cos(theta+(4pi)/3)` , then write the value of `1/x+1/y+1/zdot`

If x cos theta=y cos(theta+(2 pi)/(3))=z cos(theta+(4 pi)/(3)), then write the value of (1)/(x)+(1)/(y)=(1)/(z)

If xcostheta=ycos(theta+(2pi)/3)=zcos(theta+(4pi)/3) then the value of 1/x+1/y+1/z is equal to

If x/(costheta)=y/(cos(theta-(2pi)/3))=z/(cos(theta+(2pi)/3)) then x+y+z is

If x cos theta = y cos (theta + (2pi)/(3)) = z cos (theta + (4pi)/(3)) , find the value of xy + yz + zx

If x costheta=y cos (theta+(2pi)/3)=z cos(theta+(4pi)/3) show that xy + yz+ zx = 0

If xcostheta=ycos(theta+(2pi)/3)=z cos(theta+(4pi)/3) , prove that x y+y z+z x=0.

If xcostheta=ycos(theta+(2pi)/3)=z cos(theta+(4pi)/3) , prove that x y+y z+z x=0.

If x cos theta=y cos(theta+(2 pi)/(3))=z cos(theta+(4 pi)/(3)), prove that xy+yz+zx=0