In[]:=
ClearAll[a,b,c,x,θ]​​ax+bx^2+c/.x->Exp[θIPi]
Out[]=
c+a
πθ

+b
2πθ

In[]:=
ClearAll[a,b,c,x,θ]​​aExp[θIPi]+bExp[2θIPi]+c/.Exp[θIPi]->x
Out[]=
c+b
2πθ

+ax