Yes there is. It's called a PVC snap tee and it's made for precisely
this kind of application. It's like a regular T, except the back
of the long part of the T is missing and it's sized to snap over the
existing PVC pipe. You glue it in place, then use a drill inside
the short open end to make a hole into the existing pipe.
No fuss, no muss.
Most hardware stores have what is called a slip fix telescoping connector. It
slips over the end of your pipe on wide end (use primer and glue) then uses
either a coupling or slip T on the other. The slip fix uses "O" rings to seal so
it can telescope out. Just do not use on the main line that has constant
pressure they are designed for intermittent pressure only.
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