I am not a lawyer, and this is not legal advice. You should hire an attorney who can advise you on the correct course of action. The following are, to my knowledge, the steps required to meet the requirements of both licenses.
Your software must include a relatively prominent Copyright notice that says something to the effect:
This software includes code from: AngularJS, Copyright (C) 2010-2012 Google, Inc., and Karyon, Copyright (C) 2013 Netflix, Inc.
Then, you must also include a copy of the MIT license shipped with AngularJS (the license requires that the Copyright notice and the license's warranty notice are both included in all copies) and the Apache License from Karyon (which also requires a notice of the Copyright and the warranty disclaimer). Both of these licenses should be copied, in full, into a file called
NOTICES included in your project.
You are free to distribute the code under whatever open source license you see fit, not including the GPL or LGPL versions 1 or 2, or any other similar Copyleft license (GPLv3 is fine, as it's compatible with Apache v2). I recommend continuing to use the Apache v2 license. The license you choose to use should be placed in a file called
LICENSE included in your project.
Again, I recommend consulting an attorney to ensure that you've met all requirements of the Apache license, before redistribution.