Why Do Second and Third Order Spectra Overlap in Diffraction Grating?

[Nemo's]

Homework Statement

White light is incident normally on a diffraction grating with slit separation d of 2.00x10^-6m.
a)Calculate the angle between the red and violet ends of the first-order spectrum. The visible spectrum has wavelength between 400nm and 700nm.
b)Explain why the second and the third order spectra overlap.

Homework Equations

sinθ=nλ/d

The Attempt at a Solution

I was able to solve part (a) by substituting in the above formula with λ=700nm for red and λ=400nm for violet.
However I don't really know how to explain (b) I was thinking that for the next spectrum the path difference for red would be 1 complete wavelength so 400+400=800, for violet 700+700=1400.
For the third spectrum the path difference would be for red 400+400+400= 1200.
So violet from 2nd spectrum seems to be interfering with red from the 3rd spectrum.
I know this isn't the correct answer so can someone please help ?

 

[technician]

calculate the angle for the red in the second order spectrum (the 'end' of the second order spectrum)
calculate the angle of the blue in the third order spectrum (the 'start' of the third order spectrum)
What do you notice about these angles?...can you explain?

 

[Nemo's]

So how do I calculate the angle for the 2nd spectrum? can I use λ =800 for violet and λ=1400 for red

 

[Nemo's]

O.K I got it the angle for red in the 2nd spectrum would be approx. 44.4° and that for violet in the third spectrum would be approx. 36.9° so the second and third spectra overlap.
Thank you :)