Reflection and Transmission at oblique incidence Griffiths

I’m working through Griffiths E&M and on page 408 he gives the boundary conditions for oblique incidence. I’ve spent an hour trying to understand how he goes from the boundary condition $$\epsilon_1(\textbf{E}_{0I} + \textbf{E}_{0R})_z = \epsilon_2(\textbf{E}_{0T})_z$$ to $$\epsilon_1(-E_{0I}\sin{\theta_I}+E_{0R}\sin{\theta_R})=\epsilon_2(-E_{0T}\sin{\theta_T})$$

And I must say I’m miffed. Any help greatly appreciated...

• Please let us know what's got you miffed. Perhaps fill in the steps that you would take, and show how you get a different answer. It's hard to help when we don't know what the sticking point is. Jul 29 '19 at 2:00

I'm guessing that your confusion has to do with not noticing or misinterpreting the subscript "z" in the first equation. It means take the z component of the vector, hence the $$\sin(\theta)$$ on both sides (the opposite signs on the left side have to do with directions).