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Sadly we now know this is not the case.... It depends on your skin type. If you have dark skin (e.g. you have African heritage) then your skin will contain eumelanin, which is the best type of pigment for UV protection.
On the other hand If you have fair skin, lying on the beach to earn that tan will create Pheomelanin. Pheomelanin is far less stable then Eumelanin and can even break down when exposed to UV rays generating free-radicals in the skin.