# 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?

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