# Why does small angle approximation work for Young's double slit and not for single/multiple slits?

I understand that for a double slit experiment the equation is $$\lambda=xd/L$$, which has come from the small angle approximation of $$d\sin\theta = n\lambda$$ by assuming that $$\sin\theta = (x/L)$$ and therefore can be subbed in. I don't get why this doesn't work for both single slit diffraction and especially multiple slit diffraction. Can anyone explain?

To add some numbers to @PhilipWood's correct answer, a typical diffraction grating has around 250 lines per mm. In other words, the distance between the "slits" is $$d=0.004$$ mm $$= 4\times 10^{-6}$$m.
Suppose you were doing an experiment with a green laser ($$\lambda \approx 500$$ nm = $$5 \times 10^{-7}$$ m). The grating equation tells us that the maxima appear at $$\sin{\theta} = \frac{n \lambda}{d} = 0.125\, n.$$
Plotting $$\theta$$ and $$\sin{\theta}$$ for different orders, we'd get a graph like the one below, and you should be able to see that for values of $$n > 4$$, the approximation stops being very faithful! $$\sin \theta = \frac{x}{L},$$ then $$x$$ would never be greater than $$L$$. However, anyone who's actually done an experiment with a diffraction grating and a laser will be able to tell you that it's not very hard to have $$x > L$$ for large $$n$$.
It's not because of the multiple slits in the grating, but because the slits are much closer together than Young's slits. This means that for the grating the non-zero-order constructive interference 'fringes' are at much greater angles, $$\theta$$, to the normal than for Young's fringes. Whereas for Young's fringes the angles are small enough to use the approximation, $$\sin \theta \approx \theta \approx \tan \theta=\frac xL,$$ for the grating the angles are too large for the approximation to be applicable.