/dev/sda1  *         windows-install
/dev/sda2         windows
/dev/sda3       1756385280 1757409279    1024000   500M 83 Linux
/dev/sda4       1757411326 1953523711  196112386  93.5G  5 Extended
/dev/sda5       1757411328 1945491455  188080128  89.7G 8e Linux LVM
/dev/sda6       1945493504 1953523711    8030208   3.8G 8e Linux LVM




This is the aimed following steps:
>sudo mount /dev/sda2 /mnt #Replace sda2 with your partition number
>for i in /sys /proc /run /dev; do sudo mount --bind "$i" "/mnt$i"; done
>sudo chroot /mnt
>update-grub