Laurent Series of $f(z)=(z+1)\sin\frac{z^{2}+2z+5}{(z+1)^{2}}$ We are asked to find the Laurent series for the following function.
$$f(z)=(z+1)\sin\frac{z^{2}+2z+5}{(z+1)^{2}}$$
Around the point $$z_{0}=-1$$
I have tried to factor the inside of sine, to no avail.
I know that $\sin(z)$ at $z=0$ is a simple pole, even if the inside is a square like $(z+1)^2$.
Furthermore, I think term $(z+1)$ multiplied by sine, might be suggestive of a derivative of some sort.
Other than that, I am lost as far as what to do with the inside of sine. 
Any help would be appreciated!

Here are some hints:


*

*$z^2+2z+5 = (z+1)^2+4$

*Use a Taylor series of sine, but not the usual one.
I think this should be enough to get you started. If you have no idea how to use these hints, I can give you more hints.

Edit #1.
I thought making "one" italics would be a good hint...
Basically, I was suggesting that you use the Taylor series of sin centered at 1.
But @Santosh Linkha's comment might work better, since you'll be able to use the Maclaurin series of sin and cos.
In either case, you'll have $\sin(1)$ and $\cos(1)$ appear as coefficients of your series.
