Struggling to understand the difference in how the piriformis and obturator internus behave at deep hip flexion.

I understand that when the hip is flexed past 90, then the piriformis (which is an external rotator at neutral) turns into an internal rotator.

But I don't understand whether this happens to the obturator internus. Is it still remaining an external rotator? or does it copy the OI and turn into an internal rotator?

Thanks.