AMC 10 2017a Problem 13

Define a sequence recursively by $F_{0}=0,~F_{1}=1,$ and $F_{n}=$ the remainder when $F_{n-1}+F_{n-2}$ is divided by $3,$ for all $n\geq 2.$ Thus the sequence starts $0,1,1,2,0,2,\ldots$ What is $F_{2017}+F_{2018}+F_{2019}+F_{2020}+F_{2021}+F_{2022}+F_{2023}+F_{2024}?$ $\textbf{(A)}\ 6 \textbf{(B)}\ 7 \textbf{(C)}\ 8 \textbf{(D)}\ 9 \textbf{(E)}\ 10$