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SQL 2012 on a Windows 2008 R2 cluster, would like to upgrade Windows to 2012 R2

I need someone to help validate a strategy. I have a pair of Windows 2008 R2 server in a active/passive failover cluster with SQL 2012 installed. I would like to upgrade the Windows OS to 2012 R2. I know that you cannot join a Windows 2012 R2 server to a 2008 R2 cluster. I thought about evicting a node and doing a fresh install of Windows 2012 R2 with cluster services, then detach the databases from SQL, destroy the 2008 R2 windows cluster, build the 2012 R2 cluster using the same name, IP, and SAN drives, then install SQL 2012 as a cluster using the same instance name and attaching the databases.