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"dans le sens horaire " and "dans le sens anti-horaire " seem to be less of a mouthful.
I see that you can also just say "sens horaire" ,perhaps as a stand alone phrase.
"En sen horaire " is also shown but I am not sure when you would use it.
dans le sens des aiguilles d'une montre/ dans le sens inverse des aiguilles d'une montre are the most common phrases
perhaps less common dans le sens horaire is fine too but although dans le sens anti-horaire is correct it doesn't sound as quite natural.