Spread rotation is buried rather deeply in the menus, as you can see in the following screenshot:
This is very tedious, but fortunately it's not too difficult to move those rotation items up into the main Pages context menu:
(For somewhat reason it's not possible to get the 180° menu item there; probably a bug, but rotating 90 degrees twice makes up for that.)
When the spread was rotated, the Clear Rotation item is added:
Run the script, linked below, just once. The change in the Pages context menu is stored with InDesign's preferences when you exit InDesign and is reinstated next time you start InDesign. Only when you trash InDesign's preferences (by starting it while holding down Alt+Ctrl+Del) will you need to run the script again.
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3 June 2017: The script now works in all localisations.
28 Jan. 2017: The script stopped working in some circumstances. Fixed.
27 Mar. 2016: Posted.
Show script (right click, Save Link/Target As to download)
Installing and running scripts
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