integrate Sin (z Sin t) , etc

hi all, i need some help to solve this problem..(Nod)

i knew we have to make the equation with jacobi-anger expansion,

so that we get the series form of that equation, and then integrate it

but i cant find the exact jacobi-anger expansion in any web for sin(z sin t) sin(z cos t) cos(z sin t) sin(z sin t) (Headbang)

i tried wiki but i think it doesnt correct (Doh)

so, please help me find the RIGHT expansion, or any of you guys have a different method to solve it?

thank you very much