It is given that
4cosec²2θ - sec²θ ≡ cosec²θ, θ ≠ nπ/2, n ∈ Z.
a) Prove the validity of the above trigonometric identity.
b) Hence show that if
4(cosec²2θ - 2) = sec²θ - 2cosecθ,
then either sinθ = 1/2 or sinθ = -1/4.