# Applying Sylvester's theorem in quantum mechanics

A $$2d$$ system consists of $$N$$ identical cells arranged linearly in series. The transfer matrix of a single cell is an unitary Hermitian $$2$$x$$2$$ matrix with eigenvalues $$\exp(±i\theta)$$.

I need to use Sylvester's theorem to deduce the values of $$\theta$$ , for which the transmission coefficient through the system is equal to $$1$$. Can anybody help me on how to apply it, any formulas? My professor gave us this problem, but he never mentioned Sylvester's theorem. I searched online but I got confused.