This is a bit of a trick question! It's impossible for neither half of the Earth to be tilted towards the sun. Here's why:

* Earth's Tilt: The Earth is tilted on its axis at approximately 23.5 degrees. This tilt is the reason we have seasons.

* Seasons: The tilted Earth means that different parts of the planet receive varying amounts of direct sunlight throughout the year. One hemisphere is always tilted towards the sun (experiencing summer) while the other is tilted away (experiencing winter).

So, there isn't a month where neither half is tilted towards the sun. There is always one hemisphere that is tilted closer to the sun than the other.