How do you solve this trig identity problem without factoring?

Question

I just used @ to represent theta:

sin^4@ + 2sin^2@cos^2@ + cos^4@ = 1

Answer 1

sin^4 + 2sin^2 cos^2 + cos^4 = (sin^2 + cos^2)^2
1^2 = 1

Answer 2

Didn't you just factor that? (perfect square trinomial)

I'm looking for a way to solve it without factoring..