# inspiration:- Mistakes give rise to problems!

**Geometry**Level 4

\[\large\sin(x+y)=\sin(x)+\sin(y)\] We know that the above splitting is not allowed. This is a false property, it will be a mistake if you do it! But for how many ordered pairs \((x,y)\), where \(x\) and \(y\) are integral multiples of \(\pi\) and \(-\pi\leq x,y\leq 3\pi\), does the above equality seem to hold true?