First, please use math template, it is very frustrating to read something like this, and ask a precise question, I assume you want to find theta but I am not a mind reader.
#frac{sin(theta)}{1+cos(theta)}=frac{1-cos(theta)}{sin(theta)}#
We can suppose #1+cos(theta)# and #sin(theta)# to be nonzero, otherwise the expression does not make sense, so we can multiply by #1+cos(theta)sin(theta)# and get
#sin^2(theta)=(1-cos(theta))(1+cos(theta))=1-cos^2(theta)=sin^2(theta)#
So we get the tautology #sin^2(theta)=sin^2(theta)#, true for all #theta# that make sense, so we just need to exclude the ones such that #sin(theta)=0# and #cos(theta)=-1#. So #theta ne npi# and #theta ne (2n+1)pi#, in particular since the second is weaker then the first we conclude.
