How to mount 18mm MDF Shelves on plasterboard/drywall hollow wall (no studs)?
I love those ez anchors they can support a fair load. 
At 77” long and only 7” deep I would consider L brackets that require 2 screws each this would provide ~100 lbs of support at each bracket l bracket is similar to your angle but one side is 3” the other is 1” or 1/2 my local big box store has this type of angle or bracket. The issue here is the front will sag so a longer bracket is really needed.  As far as how many you will need I would think at least 5 brackets because MDF will sag if not supported. 4 may work but I would probably use 5 . 

I would create triangle braces out of 1x2  again I would probably use 2 anchors for each support 7 “ is not much but better safe than sorry. 
If you make your triangle 7” on the 2 sides then the long side creates the support for the front of the shelf , this would prevent sagging.