Use the Pythagorean identity: $\sin^2\theta + \cos^2\theta = 1$ for any angle $\theta$.

Substituting $2\theta$ for $\theta$:

$\sin^2(2\theta) + \cos^2(2\theta) = 1$

Therefore:

$3[\sin^2(2\theta) + \cos^2(2\theta)] = 3(1) = 3$