Light travelling through several polarizers

[Jufro]

Homework Statement

This is problem 71, chapter 38 in Physics for Scientists and Engineers 8th edition by Serway/Jewett.

Three polarizers are situated in a straight line with one spinning in the middle with θ=ωt.
Find the intensity of light coming out the other side as a function of time.
The attachment is the diagram of the system.

Homework Equations

Manus's Law: I = I_max cos² θ. Where θ is the angle between the transmission axis for the two polarizers.

The Attempt at a Solution

Through the first two polarizers we have:
I= I_max cos² θ = I_max cos² ωt
which becomes
I= I_max/2 (1+ cos(2ωt))

Then the light from the second polarizer is:
I= I_max/2 (1+ cos(2ωt)) cos² (90-ωt)= I_max/2 (1+ cos(2ωt)) sin² (ωt)

and this turns into:
I_max/4 (1+ cos(2ωt))(1- cos(2ωt))
I_max/4 (1- cos² (2ωt))
I_max/4 (1-(1+cos(4ωt)/2))
And for the answer we have:
I_max/8 (1- cos(4ωt))

The problem is the book expects the solution to be:
I_max/16 (1- cos(4ωt))

So I am off by a factor of 2. Can anyone see my problem or could it be a typo?

 

[rude man]

Please provide the attachment.

 

[Jufro]

Must not have clicked upload the first time.

 

[haruspex]

What would the intensity be with only one polariser?

 

[Jufro]

*face to palm* Thanks Haruspex