Square taper bottom bracket installation

Hi
New to the forum and already gathered plenty of info.
But.... I'm changing out bottom bracket and the cup is being a pain but soaking in penetrating oil as I type.
I will get the bleeder out eventually!!
Anyway to stop the BB & cup sticking in the future should I grease the threads of both the BB & cup when reinstalling?
As I know to put grease on the crankset/crank arm and bolts.
I imagine the answer to be yes but I just want to make sure for peace of mind.
Thanks in advance
New to the forum and already gathered plenty of info.
But.... I'm changing out bottom bracket and the cup is being a pain but soaking in penetrating oil as I type.
I will get the bleeder out eventually!!
Anyway to stop the BB & cup sticking in the future should I grease the threads of both the BB & cup when reinstalling?
As I know to put grease on the crankset/crank arm and bolts.
I imagine the answer to be yes but I just want to make sure for peace of mind.
Thanks in advance
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Drive side is reverse thread so clockwise to remove.
And it all promised so so much”
Giant Trance 2 27.5 2016 ¦ Sonder Broken Road 2021¦ Giant Revolt Advanced 2 2019 ¦ Giant Toughtroad SLR 1 2019 ¦ Giant Anthem 3 2015 ¦ Specialized Myka Comp FSR 2009
A soaking and brute force sorted that
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Marin Hawk Hill 2 2018
Kinesis Tripster AT, SRAM Apex
Specialized Crossroads 2000