Consider $\displaystyle f(z) = \frac{e^{z}(1- \cos(z))^{2}}{\sin (z)^{3} z^{3}} $

Now the numerator has 4 zeroes. And the denominator has 6 zeroes? And $\displaystyle \sin z $ and $\displaystyle z $ have triple zeroes in the denominator?

Thus $\displaystyle f $ has a double pole at $\displaystyle 0 $?

Is this correct?