Microsoft doesn't break grub, it does what is known as a "bootloader coup". rEFInd is an easy way to fix without having to google magical console incantation after booting in an installer liveusb and then chrooting into the broken system
You USB boot that rEFInd stick and choose " install rEFInd" and you're done.
The only catch is the rEFInd is kind of a maze to find the rEFInd .iso
It is here
http://sourceforge.net/projects/refind/files/0.14.2/refind-flashdrive-0.14.2.zip/download