past perfect - "Get used" vs "got used"

I'm learning English grammar with the book by Raymond Murphy: English Grammar in Use [3rd Edition]. In the exercises for unit 61, I have to complete the sentences using used to. I can't understand why I have to say get used to living instead of got used to living for this example:

Sue moved from a big house to a much smaller one. She found it strange at first. She had to __________ in a much smaller house.

Is it past simple or past perfect?

Answer

I can see why this would be confusing.

• She would have to get used to living in a smaller house.


• She had to get used to living in a smaller house.


• She had gotten used to living in a smaller house.


• She got used to living in a smaller house.

All of these are acceptable. Each has a slightly different time reference; the first one is looking ahead, and the last two are looking back.

As Brett indicated, the problem with the one in the book (had to got used to) is you don't use "got" after "to".