`sin^(2)(pi)/(4)+sin^(2)(3 pi)/(4)+sin^(2)(5 pi)/(4)+sin^(2)(7 pi)/(4)=2`

The value of (sin^(2)(pi)/(10)+sin^(2)(4 pi)/(10)+sin^(2)(6 pi)/(10)+sin^(2)(9 pi)/(10)) is

(cos^(2)pi)/(8)+(sin^(2)(3 pi))/(8)+(sin^(2)(5 pi))/(8_(sin)^(2))(7 pi)/(8)=2

sin(pi)/(4)*sin(3 pi)/(4)*sin(5 pi)/(4)*sin(7 pi)/(4)=

Prove that: (sin^(2)pi)/(18)+(sin^(2)pi)/(9)+(sin^(2)(7 pi))/(18)+(sin^(2)(4 pi))/(9)=2

Prove that: sin^(4)((pi)/(8))+sin^(4)((3 pi)/(8))+sin^(4)((5 pi)/(8))+sin^(4)((7 pi)/(8))=(3)/(2)

(sec^(2)(pi)/(4)-cot^(2)(pi)/(4))/(sin^(2)(pi)/(3)+cos^(2)(pi)/(6))+(sin^(2)(pi)/(2)-cos^(2)(pi)/(3))/((1)/(4)tan^(2)(pi)/(6))=9(2)/(3)

Prove that the value of each the following determinants is zero: sin^(2)(x+(3 pi)/(2))quad sin^(2)(x+(5 pi)/(2))quad sin^(2)(x+(7 pi)/(2))sin(x+(3 pi)/(2))quad sin(x+(5 pi)/(2))quad sin(x+(7 pi)/(2))sin(x-(3 pi)/(2))quad sin(x-(5 pi)/(2))quad sin(x-(7 pi)/(2))