Answer
The Fundamental Theorem of Calculus does not apply (for step 1).
Work Step by Step
Th.4.9 The Fundamental Theorem of Calculus:
If a function $f$ is CONTINUOUS on the closed interval $[a, b]$ and $F$ is an antiderivative of $f$ on the interval $[a, b]$, then
$\displaystyle \int_{\mathit{0}}^{b}f(x)dx=F(b)-F(a)$.
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We may apply the FTC when $f(x)=\csc x\cot x $ is continuous on the closed interval $[a, b]$
$f(x)=\csc x\cot x$ is not continuous on $[\displaystyle \frac{\pi}{2}, \displaystyle \frac{3\pi}{2}]..$
It has a nonremovable discontinuity at $ x=\pi$.
So, the first step is not allowed, as the theorem does not apply here.
