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Periodic function Roots

Hello, I'm trying to solve an periodic ecuation involving several harmonics
(Style ACos(x)+BCos(2x)+...==K). Mathematica can't let me us  'Solve'
function, so it gives me the error:
Solve::tdep: The equations appear to involve the variables to be solved for
in an essentially non-algebraic way.

To arrange this, i'm making a little program involving FindRoot function to
find at least two roots from the ecuation in the first period. But I would
like to know if there are some other method to do this more easily.

Thanks a lot

F. Bellas

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