Include shortcode in shortcode?

I need to be able to append the current date to an API request. I can get that using the Current Date plugin but JSON Content Importer doesn’t seem to like there being another shortcode inside its shortcode:

[jsoncontentimporter url=https://xxxxxxxxx/json?lat=53.06859256033253&lng=-4.076224835463193&date=[current_date format='Y-m-d'] basenode=results]
sunrise={sunrise} /// sunset={sunset}
[/jsoncontentimporter]