It depends on your local plumbing code.
The UPC plumbing code requires a vent within fix feet.
If a lav or shower is close, you can use that to "wet vent" if the pipe is 2" or larger.
If the stack in your picture is serving as the waste stack for the upstairs plumbing, then it can't be used as a vent. You will need to run a separate vent up through the roof.
Venting on trap arms