Calculation of matrix element for ##e^{+}e##-->##\mu^{+}\mu##

[dark_matter_is_neat]

Homework Statement

This is problem 5.4 from Schwartz's QFT and The Standard Model
It for me to calculate the matrix element of $e^{+}e$-->$\mu^{+}mu$ in the ultra relativistic limit in the center of mass frame using circular polarization instead of linear polarization which was done in section 5.3.

Relevant Equations

Setting the $e^{+}e$ axis as the z axis, the initial momentum vectors are:
p1 = (E, 0, 0, E), p2 = (E, 0, 0, -E)
The initial circular polarization vectors should be:
$\epsilon 1 = \frac{1}{\sqrt{2}}(0,1,i,0)$ and $\epsilon 2 = \frac{1}{\sqrt{2}}(0,1,-i,0)$
The final momentum vectors will be at some angle with respect to the z axis, so I will pick for these vectors to be rotated around the x axis by some angle $\theta$.
So the final momentum vectors are:
p3 = E$(1, 0, sin\theta, cos\theta)$ and p4 = E$(1, 0, -sin\theta, -cos\theta)$
The final circular polarization vectors should be the initial polarization vectors operated on by the same rotation so they should be:
$\epsilon 3 = \frac{1}{\sqrt{2}}(0,1,icos\theta,-isin\theta)$ and $\epsilon 4 = \frac{1}{\sqrt{2}}(0, 1, -icos\theta, isin\theta)$

Following the calculation done in section 5.3 of Schwartz's QFT and The Standard Model, the matrix element, M, should have two contributions M1 and M2.
M1=ϵ1ϵ3+ϵ1ϵ4
M2=ϵ2ϵ3+ϵ2ϵ4
However when I do these calculations I get that M1 = M2 = 1, $|M|^{2} = |M1|^{2} + |M2|^{2} = 1+1 = 2$, which does not match with the result obtained from using linear polarization: $|M|^{2} = 1+cos^{2}\theta$
I'm not really sure where the calculation is going wrong, this should match with the linear polarization result.