'In addition' is a preposition which adds information presented in one sentence to the information in another sentence. In this particular case, the advantages of listening to music are listed both in sentences 2 and 3. The first advantage mentioned is that listening to music eliminates distractions (sentence 2), while the second advantage is that music helps with relaxation and stress relief (sentence 3).
'However' should be used when we introduce an idea that is in contrast to what is previously claimed, hence it is not the appropriate choice here.
'The fact is' is not the right choice either, as it is used to summarize the most important point of what has been said.
'As a result' is used when we list the consequences of a particular phenomenon, which we do not do in sentence 3.
