Changing read permissions on /private/etc recursively

Changing read permissions on /private/etc recursively

I was trying to make my /private/etc folder and all its contents
world-readable. 'Permission denied' messages from a number of internal
files and folders were a recurrent theme whenever I did a find operation
on that folder. But chmod -R seems to have failed here. Can someone please
explain why I get this error message and what I should do to fix it? I'm
on OS X 10.8.3.
$ sudo chmod -R a+r /private/etc
sudo: /private/etc/sudoers is mode 0444, should be 0440
sudo: no valid sudoers sources found, quitting