You can do it with the picture ratio. Best photo quality is 3:4, so if it's on this setting, apple adjusts the view so it displays the entire photo while maintaining the aspect ratio. I'm pretty sure you can use that to calculate the height like this:
CGFloat screenWidth = [UIScreen mainScreen].bounds.size.width;
// at current screenwidth, 'previewHeight' is the height necessary to maintain the aspect ratio
CGFloat previewHeight = screenWidth + (screenWidth / 3);
CGFloat screenHeight = [UIScreen mainScreen].bounds.size.height;
CGFloat totalBlack = screenHeight - previewHeight;
CGFloat heightOfBlackTopAndBottom = totalBlack / 2;
NSLog(@"Height is: %f", heightOfBlackTopAndBottom);
It could probably be more optimized, but I think this is more clear for demonstration of what is happening. Also be aware of potential differences in landscape mode.