Brad believes in music for its therapeutic effect on unhappy people is that a transitive or intransitive verb

It would be transitive.  A transitive has a direct object, something that it the verb is acting on.  The verb is belive.  The direct object is what it's acting on, so, what is he believing?  In music.  He is believing on the music, so since it has a direct object, it's transitive.

It would be intransitive if it didn't have a direct object:

I believe.
He believed.

But as soon as you add any kind of direct object it's transitive:

I believed him.
He believed the dog.