Cantorvals as sets of subsums for a series connected with trigonometric functions

We study properties of the set of subsums for a convergent series $k_1\sin x+\cdots +k_m\sin x+\cdots +k_1\sin x^n+\cdots +k_m\sin x^n+\dots$, where $k_1,k_2,k_3,\dots ,k_m$ are fixed positive integers and $0<x<1$. Depends on parameter $x$ this set can be a finite union of closed intervals or Cantor-type set or even Cantorval.