How to safely delete 800 million records and free up space on database

Yeah. So. My boss thought it was a good idea to add every request and it's form data to a table he would be using for statistics. This was done 5-6 years ago.

This one website that is heavily used is now using up almost 600Gb for one table, and will soon be maxing out the server disk.

As every great leader, he has delegated the job to poor little developer me. It is now my responsibility to free up a lot of space but not breaking the statistics software he built on top of it.
I was given permission to delete all records for users that have been inactive for 6 months which is almost 700 million records.

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How would I do this in the most efficient way not maxing out the log which would use up the last 100Gb of space on the server.