I wrote this since I always forget the 2 essential steps in order to regain root on a Nexus 10 device which has been updated over-the-air. Basically you’ll have to flash a new recovery image:

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# ~/android-sdk/platform-tools/fastboot flash recovery recovery-clockwork-touch-6.0.4.3-manta.img
...

Before booting into recovery make sure you’ll push the latest SuperSU zip package to your device:

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# adb push UPDATE-SuperSU-v1.51.zip /mnt/sdcard
...

Boot into recovery:

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# adb reboot recovery
...

In CWRM install the previously pushed zip file and you’re done.