DJeroen

One of they (many) ways to fix this is as follows:
 
First straiten your picture and the checkered triangles in the corners will show, showing transparency, meaning no basis to paint on.
Like in real life, when you rotate a painting, there is nothing to paint on, since the material moved, here is how to fix it.
 
Duplicate the background layer and add a new pixel layer, set all layer visibility to invisible, apart from the new pixel layer (which should be in-between of the original and duplicate background layer. Use the flood fill tool to paint the pixel layer white.
 
Select the duplicate background set visibility of the duplicate background layer to on. (the checkered area's are now shown in white)
 
By now you should have 3 layers in total (in this order, bottom to top), background (invisible), the white pixel layer (visible) and the duplicate background layer (visible).
 
Select the 2 visible layers and right click to open the menu, select merge visible.
 
This creates a new layer with the original dimensions of your picture where the checkered area's are now filled with white. We created something to paint on!
 
Here comes the reward: select the inpainting toolbrush and fill the 4 triangles in the corners :-)
 
You may have to experiment with the inpaining brush options for the best result, depending on the context area, if the brush size is to big you get unwanted artefacts.