How can I pre-set values for coefficients in a sine series curve fit?

I'm trying to fit a sine series through my data. From the sine series, which consists of

a_1*cos(b_1*x + c_1) + ... + a_n*cos(b_1*x + c_n)

I would like to use all the coefficients a_n for further calculations. However, to get the correct values for those coefficients, I'd like to set b_n=1 and c_n=0.

I've tried feeding the fit with Startvalues (NaN, 1, 0) and both upper and lower boundary conditions (Inf, 1, 0), but that only gives very bad fits.

How can I set those coefficients?