Experimental: Exercise Therapy

This group will receive the Shape Up My Shoulders (SUMS) protocol and it will be led by a physiotherapist trained in therapeutic exercise. It will last 12 weeks and it will be divided in 3 stages.~Stage I- Early-stage rehabilitation exercises (i.e., breathing and relaxation exercises, ball rolling exercises, hand gripping exercises, mental imagery and contralateral side exercises) and Shoulder Symptom Modification Procedure (SSMP). This stage typically lasts 1 to 2 weeks.~Stage II - Isometric, eccentric and heavy slow resistance exercises. The final part of Stage II is a progression from eccentric only to eccentric and concentric contractions.~Stage III - Functional program. This stage starts in week 5 or 6 and progressed to week 12. Involves pushing, pulling, throwing, lifting, carrying, and precision (sensory-motor control) exercises.

Active_comparator: Extracorporeal Shockwave Therapy

This group will receive high energy Extracorporeal Shockwave Therapy (ESWT) applied by an experienced physiotherapist. ESWT will be applied on the most tender point of the shoulder, located by palpation. The dose will be 1500 impulses per session without anaesthesia and an intensity between 0.15 and 0.30 mJ/mm2 depending on patient tolerance. A total of 4 treatment sessions (1 session per week) with 1 week of rest between sessions will be implemented. Patient's position during the treatment will be seated in supine position with shoulder hyperextension and internal rotation with the hand placed below the contralateral glute with the palm touching the table.

Active_comparator: Ultrasound-Guided Percutaneous Irrigation

This intervention will be performed by an experienced interventionist radiologist in two sessions. The shoulder position will be with hyperextension and internal rotation with the hand behind the back. One 20 mL syringe with saline solution, one with an anaesthetic with 20 mg/mL of mepivacaine 2% and another syringe with a corticoid injection with 40 mg/mL of triamcinolone acetonide will be prepared before the intervention. Firstly, the anaesthetic will be injected directed to the calcification. Then, the procedure will consist of injecting saline solution and aspiring the calcific deposits until it is neither possible to aspire more inside the syringe nor to detect any calcifications with ultrasound imaging. After that, a corticoid will be injected to the bursa to prevent the appearance of subacromial bursitis. Finally, an anaesthetic will be injected during the extraction of the needle.

No_intervention: Wait and Watch group

The wait and see group will not receive any intervention and will serve as a control group to determine the natural history of RCCT. If one treatment proves to be more effective then participants in the other groups will be offered that treatment after 12 months, or before, if the investigation finishes early due to an obvious group difference and a need to break randomisation codes.