LHS:-

   LET Y=8COSXCOS2XCOS4X

MULTIPLYING BY SINX,

  YSINX=4[2]SINXCOSX[COS2XCOS4X]

            =4[SIN2X]COS2XCOS4X

            =2[2]SIN2XCOS2X[COS4X]

            =2[SIN4X]COS4X

             =SIN8X

           Y=SIN8X/SINX------------------------eq1

hence,sin8x/sinx=sin6x/sinx

          sin8x=sin6x------------------------------eq2

when we put x=0,the eq is satisfied.please rate me if it is correct.

            x=0[principal solution]

CHEERS!