How can I make my dyed red hair darker ?

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I recently dyed my naturally brown hair to auburn with dark red highlights. However, after a day in the sun, the highlights at the top of my head have become noticeably lighter. Is there a way to reverse this and make my hair darker (more browny, less red)? And if not, how long will I have to wait until I can re-dye my hair to a natural colour such as black or brown ?