nlm = NonlinearModelFit[Data, a*Cos[2Pi*x]+(-a*Tan[phase1])*Sin[2Pi*x]+c*Cos[4Pi*x]+(-c*Tan[phase2]*Sin[4Pi*x]+e,{a,phase1,c,phase2,e},x]

MSE = nlm["ANOVATableMeanSquares"][[2]]

nlm2 = NonlinearModelFit[Data, a*Cos[2Pi*x]+(-a*Tan[phase1 + AddedPhase])*Sin[2Pi*x]+c*Cos[4Pi*x]+(-c*Tan[phase2+2*AddedPhase]*Sin[4Pi*x]+e,{a,c,e},x]