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I hate arriving late for movies now, and would never watch one in the broken fashion I used to.

I know what the sentence means. But, grammatically, how do you explain the connection of '
I used to' to the main clause?
Comments  
I think it's just a normal relative clause. There's an implied "that" ahead of "I used to". Is that what you were concerned with?

I hate arriving late for movies now, and would never watch one in the broken fashion that I used to.

Not a grammarian. Just a half-baked native speaker.
Several words are implicit.

I hate arriving late for movies now, and would never watch one in the broken fashion in which I used to watch them.

Used to watch means was in the habit or custom of watching.

in which I used to watch them is an adjective clause which modifies fashion. in which is a connecting phrase that specifies "...the realtionship of the subordinate clause to some other part of the sentence [fashion]." ---Understanding Grammar, by Paul Roberts

PS
I was so long putting this together that I did not see
Erin Zale's post.
Students: We have free audio pronunciation exercises.
Thank you for the clear explanation!