f(2006)+f(2007)+f(2008)+f(2009)
=sin(2006π/2+π/4)+sin(2007x/2+π/4)+f(2004)+f(2005)
=sin(2006π/2+π/4)+sin(2007π/2+π/4)+sin(2004π/2+π/4)+sin(2005π/2+π/4)
=sin(1004π-π+π/4)+sin(1004π-π/2+π/4)+sin(1002π+π/4)+sin(1002+π/2+π/4)
=sin(-3π/4)+sin(-π/4)+sin(π/4)+sin(3π/4)
=0