The Angry Buddhist is based on Greenland's own novel, which will be released on Tuesday (April 24).
The book follows three brothers in California; one is a Buddhist cop, while another is a career criminal and a third is a congressman running for his third term.
The estranged siblings are brought back together when a shocking murder threatens to derail their lives.
Greenland - who wrote and produced on HBO's Big Love - will executive produce The Angry Buddhist alongside David Kanter (Rendition).
Showtime is also developing two new shows from Alexander Payne (The Descendants) and Peter Morgan (Frost/Nixon), as well as a possible spinoff from David Duchovny comedy-drama Californication.
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