\(|z^2 + 2z\cos\alpha| \le |z|^2 + 2|z||\cos\alpha| \le |z|^2 + 2|z|\)

\(< (\sqrt{3} - 1)^2 + 2(\sqrt{3} - 1) = (\sqrt{3} - 1)(\sqrt{3} - 1 + 2) = (\sqrt{3} - 1)(\sqrt{3} + 1) = 2\)

So the value is less than 2.

Answer: (A)