hello
excuse me if i did not send email to you because when i reviewed your post , i saw your answer is true but have a problem , you must attend to
equal sign .
please to attend :

cdf of y = 0 if arcsin< 0
arcsiny if 0 =< arcsiny < pi
1 if arcsinyy => pi
i am very very sorry that the first i didnt read your post correctly so i understand wrong your intent .
your answer was true but have a little problem that i correct it above