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functional ecuation, a bit strange, but not difficult

Source: Third Zhautykov Olympiad, Kazakhstan, 2007

April 25, 2007
functiontrigonometrygeometrygeometric transformationalgebra proposedalgebra

Problem Statement

Does there exist a function f:R→Rf: \mathbb{R}\rightarrow\mathbb{R} such that f(x+f(y))=f(x)+sin⁡yf(x+f(y))=f(x)+\sin y, for all reals x,yx,y ?
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