Note: A more detailed and user-friendly version of these instructions can be found at: http://www.oppoforums.com/threads/n5...ructions.24159
Download http://lum.uk/n3/files/recmodn3.img and http://lum.uk/n3/files/Root_ColorOS_by_tantrums_v2.zip
Copy the rooter onto your SD card.
Boot into fastboot by holding volume up while powering on the phone.
fastboot oem unlock
fastboot flash recovery recmodn3.img
fastboot boot recmodn3.img
Flash the root coloros zip file, reboot and you're rooted.
Note: This is a modified stock recovery that can flash OTAs as well as zips not signed by Oppo. If you prefer TWRP then that is available here: https://dl.twrp.me/n3/. Note that at the time of writing TWRP is unable to flash OTAs.
Thanks to [email protected] for the original root method, Arvin A. [email protected] for the fixing SuperSU to work on ColorOS, and [email protected] for providing the modified N3 recovery.