arrosh is obviously ashamed at how he fell to corruption like his father and changes his ways. he gets rid of his badass act and goes to live in solitude and meditate, through his meditation he begins to realise how idiotic and ashamed he was to fall to the corruption of the sha and through this begins to become more wise, he also has a vision of the return of the legion in which he realises he must act.
after a year or two of solitude he begins to take up a quest to redeem himself. This quest is to not an attempt to join the horde again but for his own personal gains (and maybe to save Azeroth). The vision he sees is the legion coming back and he then sets out back into the Outland (Outland revamp) and attempts to bring Illidan back to life. He tells Illidan of what he has seen and they agree to make an alliance along with their shared hatred for the legion. Illidan and Garrosh then become a badass team and also bring in the implementation of the demon hunter class.

I didn't find the right solution from the Internet.

References:
http://www.mmo-champion.com/threads/1342514-Garrosh-and-Illidan-Redemption

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