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Despite of is the same meaning as Nevertheless, but the usage is different.
Nevertheless means in spite of (or despite with no of) a condition mentioned in another clause - sometimes another sentence.
It was raining. Nevertheless he went shopping.
In spite of the rain, he went shopping.
Despite the rain he went shopping.
Mixing up in spite of with despite is a very common mistake, but it's a mistake. It was acceptable when Shakespeare did it (he wasn't mixing them up then anyway), and it's understandable now, but it's not standard and it's not to be recommended.
nevertheless 
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