You know that $\sin^{2}\left(θ\right) + \cos^{2}\left(θ\right) = 1$.  

1. What does $\sin^{2}\left(2θ\right) + \cos^{2}\left(2θ\right) =$ ?

   Hint (a):

   Let $w = 2θ$.
   What is $\sin^{2}\left(w\right) + \cos^{2}\left(w\right)$?

2. What does $\sin^2(θ^2 – 2) + \cos^2(θ^2 – 2) =$ ?

   Hint (b):

   Let $w = θ^{2} − 2$.