If cos⁡A+cos⁡B+cos⁡C=0 and cos⁡3A+cos⁡3B+cos⁡3C=λcos⁡Acos⁡Bcos⁡C then λ is

If cos⁡A+cos⁡B+cos⁡C=0 then cos3⁡A+cos3⁡B+cos3⁡C=3cos⁡Acos⁡Bcos⁡C Given cos⁡3A+cos⁡3B+cos⁡3c=λcos⁡Acos⁡Bcos⁡C4cos3⁡A−3cos⁡A+4cos3⁡B−3cos⁡B+4cos3⁡C−3cos⁡C=λcos⁡Acos⁡Bcos⁡C=4cos3⁡A+cos3⁡B+cos3⁡C−3(cos⁡A+cos⁡B+cos⁡C)=4(3cos⁡Acos⁡Bcos⁡C)−3(0)=12cos⁡Acos⁡Bcos⁡C