Please refer to the System Requirements page on the documentation to see if specific versions are supported -> https://community.dynatrace.com/community/display/...
From the looks of it, it does seem like Tomcat 8 is supported so I think you should be good. Attached picture for reference.
Have you tried at all yet? What were the results?
In addition, since it seems like you are AppMon 6.3, I would recommend you look into upgrading soon as well. Full support for 6.3 will end very soon (Aug 31, 2017). More info here -> https://community.dynatrace.com/community/display/...
Hope this helps,