Now, can you prove that the shortest night of the year is adjacent to the longest day? This is indeed the case for all latitudes, but it is wickedly difficult

Now, can you prove that the shortest night of the year is adjacent to the longest day? This is indeed the case for all latitudes, but it is wickedly difficult to prove. Hint: start by setting up an imaginary planet with irregular orbit where this is not the case. Then find what property of the orbit you needed to force that does not happen with the earth.