Find the sum of the series:

Infinte series from n=0 to infinte (-1)^n * (pi^2n+1)/(4^2n+1)(2n+1)!

i know the sin series looks like that becuase sin is

(-1)^n*x^2n+1/(2n+1)! but i dont get the 4 part in the expression, the answer is sin pi/4=1/sqrt2 but how? steps will be helpful please. thanks!