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In case $$\lambda=1$$

Prof states that measuring spin in arbitrary +n state gives me +1 as eigenvalue, what I don't understand is the next expression $$n_zα+n_−β=α$$

I have no idea how this expression comes here, please help me. The link to the lecture is given below:

http://www.lecture-notes.co.uk/suss...ments/lecture-4/spin-in-arbitrary-directions/