I think your dat can be fitted by an even function so the model could be a type of cosine Fourier series. Choose nn for how many terms you need.
dat = {{0, 0.183453}, {10, 0.18317}, {20, 0.182312}, {30,
0.180844}, {40, 0.178713}, {50, 0.175843}, {60, 0.172141}, {70,
0.167506}, {80, 0.161841}, {90, 0.155074}, {100, 0.147198}, {110,
0.138308}, {120, 0.128652}, {130, 0.118654}, {140,
0.108915}, {150, 0.100168}, {160, 0.093188}, {170,
0.0886728}, {180, 0.0871093}, {190, 0.0886728}, {200,
0.093188}, {210, 0.100168}, {220, 0.108915}, {230,
0.118654}, {240, 0.128652}, {250, 0.138308}, {260,
0.147198}, {270, 0.155074}, {280, 0.161841}, {290,
0.167506}, {300, 0.172141}, {310, 0.175843}, {320,
0.178713}, {330, 0.180844}, {340, 0.182312}, {350, 0.18317}, {360,
0.183453}};
nn = 3;
su = Sum[a[n] Cos[n Φ Degree], {n, 0, nn}];
fit = NonlinearModelFit[dat, su, Cases[su, x_a, All], Φ];
su /. fit["BestFitParameters"]
ListLinePlot[{Table[{Φ, su /. fit["BestFitParameters"]}, {Φ,
0, 360, 10}], dat}, PlotStyle -> {Gray, RedDirective[Red, Dashed]},
PlotLegends -> {"fit", "dat"}]
For nn=6 we have the following (amplitude of 6-th cosine is already very small):
