Find the limit distribution of the sequence ηn of random variables with distribution P \left( \eta_n\equal{}\arccos (\cos^2 \frac{(2j\minus{}1) \pi}{2n}) \right)\equal{}\frac 1n \;(j\equal{}1,2,...,n)\ . (arccos(.) denotes the main value.)
B. Gyires trigonometryprobability and stats