Latitude is unimportant in that type of questions.
To get from real position of 139o 46.3’E to the real position of 180o W (it is the same position as 180o E - around International Date Line) one must fly 40o 13.7' east or (which makes calculations more complicated but still possible and valid) 319o 46.3' west.
Let's assume one flies east. INS thinks that one starts at 139 o 46.3’W and flies 40o 13.7' east. Therefore INS calculates: 139o 46.3'W - 40o13.7' = 99o 32.6'W
If one flies west - INS thinks that plane starts at 139 o 46.3’W and flies 319o 46.3' west. Therefore INS calculates: 139o 46.3'W + 319o 46.3' = 459o 32.6'W = (-360oW around the globe) 99o 32.6'W.