I'm working on project that needs to tap into the toilet supply line. I've determined the best method of doing this is to TEE off the ballcock shank (The area where the supply line connects to the ballcock). The problem I'm having is trying to find a fitting to finish the part. I need a coupling that has the same 7/8" male thread on one side and any type of size on the other. I've had no luck finding fittings or adapters that would work. The OD on the straight threaded shank measures .930" (15/16) and the thread pitch is 14 threads per inch. I know there are other ways to TEE off the supply line like using barbed TEEs or tapping near the supply valve but I really need this TEE to be connected to the ballcock shank as in the diagram attached. Take a look at my diagram for a better understand of what I'm trying to do and what I need. Any help/suggestions would be appreciated.