Solar cell interference filter path difference calculation

[Wminus]

Homework Statement

See attached image, assignment a)

Homework Equations

The Attempt at a Solution

Using ordinary trigonometry, I got simply $$\Delta = sin(\theta_i) 2 d tan(\theta_t) n_{air} - 2n_{oxide} d/cos(\theta_t)$$. However, even if I apply Snell's law, it's not the answer I'm supposed to get according to the assignment. So what's happening?

The two lower triangles with the angle $\theta_t$ are identical, right?

 

[mfb]

I agree with your answer.

 

[Wminus]

I agree with your answer.

OK I'll send the professor an email. might be that the TA who made this exercise did a mistake