I start with the end

Question

I start with the end.
A sixth of a sixth

I end with the start.
A third of a third.

What am I?

Tiny Hint

Ignore the linefeeds.

Small Hint

What does the end mean?

Big Hint

It isn't a sixth of sixth, it is a sixth of a sixth.

Answer 1

You are

(a) hat

I start with the end.
A sixth of a sixth.

A sixth of "a sixth", is any one letter, and given we start with the end, our first letter is h

I end with the start.
A third of a third.

Same as the sixth, except this time it's two letters, and from the start, so a and t

What am I?

Putting all those together gives us the three-letter word hat.