Rooting a Samsung Galaxy Tab 3 10.1 - What they don't tell you

I've spent a few hours trying to root a Samsung Galaxy Tab 3.0 10.1 following instructions on the Internet. There are a few little gotchas that aren't made clear.

- You only get one chance to boot to the CWM recovery after you've flashed the device
- You don't need to press the HOME button when starting the boot

So, here is my version of the instructions:

Preparation

1. Turn on Developer Mode.
If not done already, click on Settings->About Device->Build number->Build number->Build number 
and press Build number" seven times. 
2. Turn on USB debugging.

3. Download Odin (3.07 or higher) and save it to your desktop. 

Odin

4. Download CWM Recovery and save it to your Desktop.

CWM Recovery

5. Download Root ZIP and save it to your Desktop.

Root ZIP 

Flashing

1. Extract files from Odin and CWM Recovery archives by right-clicking on each of them and selecting Extract here.

2. Open Odin ensuring you "Run as administrator".

3. Click on PDA and choose the CWM Recovery file you just extracted from the archive.

4. Make sure only the F. Reset Time boxes are checked in the Odin. De-select Auto-Reboot - otherwise you will have to be quick at engaging recovery mode. If you aren't you will end up in Android recovery, not CWM.

5. Turn OFF your device.

6. Turn it back on by holding down Volume DOWN+Power buttons together.

7. Your device should reboot into Download mode.

8. Plug in your device to your PC via USB cable.

9. Hit Start in the Odin and it’ll start flashing the recovery on your device.

10. Connect your device to your PC using the USB cable.

11. Copy the Root ZIP file from your Desktop over to the root of your SD card. Note: the SD card. Not internal memory. You will need an SD card.

12. Open a command prompt in administrator mode. Go to the android platform-tools folder and type adb reboot recovery. Alternatively turn OFF the device and turn it back on by holding down Volume UP + Power buttons together.

13. Your device should reboot into recovery mode.

14. Select install zip from sdcard followed by choose zip from sdcard.

15. Choose Root ZIP to be flashed on your device.

16. It should start flashing the file on your device.

17. Once the flashing’s done, reboot your device.

18. Go back to the menu and select reboot. If it asks you "ROM may flash stock recovery on boot. Fix?" then it will be asking you whether to reapply the stock recovery. Select Yes to keep CWM or No to return to android recovery.

Problems?

Odin stuck at initializing connection? - You didn't boot the device into download mode (POWER + VOL DOWN).

You keep booting to android recovery rather than cwm recovery? - When you've flashed using Odin it starts to automatically reboot by default. You only have the one chance to press POWER + VOL UP to enter recovery mode. If you don't do it and it goes to the normal power up sequence then install-recovery.sh will replace cwm with the stock recovery. Turn off the Auto-Reboot option in Odin and perform the reboot yourself.

Stock firmware
Stock firmware is available from the this site.