We can consider east and north direction as x and y axes respectively.
latitude 0 and longitude 0 be the origin.
Let 'a' be the total way around the world
so, if I travel east 1/3 of the way around the world, x co-ordinate = 1/3 a
if I travel north 1/3 of the way around the world, y co-ordinate = 1/3 a
So the coordinates of your new location are(1/3 a, 1/3 a)