Retin-A and wearing sunscreen inside?

I am currently six months applying Retin A daily (31, male). I live in Ireland in a town where it's prety rare to see the sun; it is always cloudy and rainy. I work inside basically from dark to dark, as days are pretty short in the winter now. My question is do I need to wear sunscreen every day, even though there's no sign of the sun and I am inside? To give you a better picture of the weather, the sun does not cast shadows.