Hello. I am located in Florida. I want to add a sink in a room on the other side of a concrete wall from the washer in the garage. The washer stand pipe ends at 3', the sink would be 33" high and would be located 2' away from the stand pipe. The stand pipe has a P trap and goes inside the concrete wall into a vent. I was planning to connect the sink drain pipe into the washer stand pipe with an additional vent OR using a double sanitary see and connecting both sink and washer with a p trap into it. The sink would be used very occasionally.
Here is a picture of the washer drain pipe
Vent view from the roof
And here is how I am planning to do it
Would that work? Is there any simpler way of adding a sink?
Here is a picture of the washer drain pipe

Vent view from the roof

And here is how I am planning to do it

Would that work? Is there any simpler way of adding a sink?