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Does ANYBODY know?
Your problem is trivial, you can just evaluate as written.
"Using continuity" just means that you recognize that the function is continuous at $\displaystyle x=\pi$ and therefore the limit can be evaluated by simple substitution.
So, the answer is 0???
$\displaystyle \lim_{x \to \pi} \; \sin(x+\sin(x)) ~=~ \sin(\pi+\sin(\pi)) ~=~ \dots $ Does it make sense now?
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