How did Christianity become the official religion of the byzanitine empire?

Byzantine Empire is a term which has been coined by historians to indicate the eastern part of the Roman Empire after the fall of the western part. The people in question did not even know this term and called their empire Roman Empire. Christianity spread though the eastern part of the Roman Empire before the fall of the western part. Christianity developed into two main forms, the Latin or Western Church and the Greek or Eastern church. The former was the main form of Christianity in the western part of the empire and the latter was the main one in the eastern part. Later they came to be called Catholic and orthodox respectively. Both these branches of Christianity became state religion in 380. Therefore,what we now call Orthodox Christianity was already the religion of the eastern part of the Roman empire before the Byzantine period.