How to to cancel Apple Music to change country?

Hi there. Recently I have changed my country and relocated to Estonia from Azerbaijan. Right now I want to change my App Store region as well, in order to use/download Europe and Estonia-specific apps too. However, when I try to change there's a pop-up that says "In order to change region first cancel your Apple Music membership". I recently, in May, purchased a yearly subscription to Apple Music and I don't want to lose my money. How can I change my region without losing my Apple Music subscription?

[Re-Titled by Moderator]