Limit and Nested Integrals

[Tolaso J Kos]

Evaluate:
$$\lim_{n \to +\infty} \int_{0}^{1}\int_{0}^{1}\cdots \int_{0}^{1}\cos^2 \left \{ \frac{\pi}{2n} \left ( x_1+x_2+x_3+\cdots+x_n \right )\right \}\,{\rm d}x_1\,{\rm d}x_2\cdots {\rm d}x_n$$


I have no solution.