AMO 2021 – Junior College (Grades 11–12) Question 1

Find $\sin^2 10^\circ+\sin^2 20^\circ+\sin^2 30^\circ+\sin^2 40^\circ+\sin^2 50^\circ+\sin^2 60^\circ+\sin^2 70^\circ+\sin^2 80^\circ$. The five choices below correspond, in order, to choices 1–5 in the original.