sinx/cos3x + sin3x/Cos9x +sin9x/cos27x +sin27x/cos81x = 0. Find x.

Dear

sinx/cos3x + sin3x/Cos9x +sin9x/cos27x +sin27x/cos81x = 0

or sinxcosx/cos3xcosx  + sin3xcos3x/Cos9xcos3x +sin9xcos9x/cos27xcos9x +sin27xcos27x/cos81xcos27x = 0

or  sin2x/cos3xcosx  + sin6x/Cos9xcos3x +sin18x/cos27xcos9x +sin54x/cos81xcos27x = 0

or  sin(3x-x)/cos3xcosx  + sin(9x-3x)/Cos9xcos3x +sin(27x-9x)/cos27xcos9x +sin(81x-27x)/cos81xcos27x = 0

0r tan3x -tanx + tan9x-tan3x + tan27x -tan9x + tan81x -tan27x =0

  tan81x - tanx =0

  tan81x = tanx

    81x = kπ + x

   x = kπ/80     where k is any intiger

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how did sin(3x-x)/cos3xcosx become  tan3x -tanx