The question

Evaluate the following integral using Cauchy Integral Formula,

$\displaystyle \oint_{|z| = 4}{\frac{e^{2iz} \ dz}{(3z - 1)^2}}$

My attempt

Not analytic at:

$\displaystyle (3z - 1)^2 = 0$

$\displaystyle z = \frac{1}{3}$

This is inside the contour, so we use CIF as follows:

$\displaystyle 2\pi i e^{\frac{2i}{3}}$

However, the solution is $\displaystyle \frac{-4\pi}{9}e^{\frac{2i}{3}}$

Where have I gone wrong? Thanks.