Contour Integral, Where am I going wrong?

[BigFlorida]

So, my book (Mathematical Methods in the Physical Sciences 3rd ed by Boas) proposed a problem that I have really been struggling with:

I know it is probably just an algebra mistake, but I have gone over it multiple times and cannot seem to find my mistake. Any ideas? The answer is supposed to be 2Pi/9.
Thank you in advance for any help.

 

[Ray Vickson]

So, my book (Mathematical Methods in the Physical Sciences 3rd ed by Boas) proposed a problem that I have really been struggling with:
View attachment 94420 View attachment 94421

I know it is probably just an algebra mistake, but I have gone over it multiple times and cannot seem to find my mistake. Any ideas? The answer is supposed to be 2Pi/9.
Thank you in advance for any help.

The image is too small and blurry to make out properly, so I will not even try. Why don't you do what others here do, and type it out?