how do I prove that ?(l,m)+?(m,n)=?(l,n)

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So I came across definition of directed angles and it really seems counterintuitive to me, i.m struggling to proof this following formula ? (l, m) + ? (m, n) = ? (l, n) as I said it seems incredibly easy thing to do, but not for stupid person like I am. It seems that I need to check so many various cases.
And in 3-dimensions I would never think that such a statement was true. So maybe I'm just too dumb, which is obvious, but I can't prove it. So if you don't mind explain to me why this is the case, I'm gonna be very grateful.