Let $R_1=\sqrt{2+\sqrt{2+\sqrt{2-\sqrt{2-\sqrt{2-...}}}}}$ be a 5-periodic nested radical, with respective sign pattern is $(++---)$.

Let $R_2, R_3, R_4, R_5$ be analogous radicals with sign patterns $(-++--)$, $(--++-)$, $(---++)$, $(+---+)$.

Find $R_1-R_5+R_2-R_4+R_3$.