Evaluate sin^2 (π/20) + sin^2 (π/10) +sin^2 (3π/20)+ ⋯ +sin^2 (π/2)

Similar SMO Senior Mock 2022 Trig Identity Gives Us Computation Reducing Vertical Axis Symmetry(math coach/educator Way Tan's cool idea to use power reducing identities) He used sin^2(x)= (1-cos(2x))/2 Also the important cos(PI-x)+cos(x)=0 since cos(PI-x)=-cos(x) is the y axis symmetry identity that avoids having to know the actual value of cos(PI/10) Math Central at University of Regina has copious trigonometry didactics. Thanks to the many student who help keeping it maintained and up to date.