We know that for complementary angles, sin (90° - θ) = cos θ.
So, sin 27° = sin (90° - 63°) = cos 63°.
Substitute this into the expression:
sin² 63° + sin² 27° = sin² 63° + cos² 63°.
Using the fundamental trigonometric identity sin² θ + cos² θ = 1, the expression simplifies to 1.