No you cannot.

What is the diameter of the stack pipe please?

The stack pipe is 1 1/2"

In Many places a laundry drain must be plummed into a 3” main or larger. you cant feed a 2” line via a reducer into a 1-1/2” and pass code. Reason being they dont want wayer backing up and you cant use the tub as an overflow basin.

Brady:

What you want to look up is called "drainage fixture unit". This is the code that assigns a value to each fixture and tells you how many of a particular fixture can drain into a particular size stack. I had to do this when I took the Florida plumber's licensing examination.

I don't have access to my book, but I can tell you you're not installing a 2" pipe into a 1 1/2" stack.