I thought "at that time" should be used when mentioning a time in the past. I guess I was wrong?
Answer from a Native speaker
They can both be used! Here either one would work. "At that time" means a previously mentioned time. It can also be used when distinguishing between two times. "At the time" means the time of something else happening. Ex: People were confused about it at that time. = People were confused about it at the time. Ex: At the time of the exam, I was well prepared for it. Ex: At that time, I was well prepared for the exam.
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