We can start by using the Pythagorean identity: sin²θ + cos²θ = 1
Since we know cosθ, we can solve for sinθ:
sin²θ + (17/8)² = 1
sin²θ = 1 - (289/64)
sin²θ = 175/64
sinθ = √(175/64)
Now, we can use the double angle formula for sine:
sin2θ = 2sinθcosθ
sin2θ = 2(√(175/64))(17/8)
sin2θ = (17/8)√(175/16)
sin2θ = (17/8)(5/2) (since √(175/16) = 5/2)
sin2θ = 85/32
Therefore, sin2θ = 85/32.