1. The problem states the trigonometric identity: $$\sin^2 \theta + \cos^2 \theta = 1$$ for any angle $\theta$. 2. This is a fundamental Pythagorean identity in trigonometry. 3. It means that the square of the sine of an angle plus the square of the cosine of the same angle always equals 1. 4. This identity comes from the Pythagorean theorem applied to a right triangle inscribed in the unit circle. 5. No matter what value $\theta$ takes, the equation holds true. 6. Therefore, $$\sin^2 \theta + \cos^2 \theta = 1$$ is always valid. Final answer: $$\sin^2 \theta + \cos^2 \theta = 1$$