$\sin ⁡x = \,?$

Alexander knew that: $$\cot x=-\frac34\ \mbox{and}\ x\in\left(\frac32\pi,2\pi\right)$$ He tried to determine the value of $\sin ⁡x$ without a calculator.

Alexander’s solution:

(1) First, he expressed $\sin^2 x$ from the formula $\sin^2 x+\cos^2 x=1$, and obtained: $$\sin^2 x=1-\cos^2 x$$

(2) Secondly, since $x\neq k\pi$, where $k\in\mathbb{Z}$, Alexander divided the expression by $\sin^2 x$ and got: $$1=\frac{1}{\sin^2 x}-\cot^2 x$$

(3) In the next step, he expressed $\sin^2 x$ from the above equation: $$\sin^2 x=\frac{1}{1+\cot^2 x}$$

(4) Subsequently, he substituted the given value $\cot x=-\frac34$: $$\sin^2 x=\frac{1}{1+\frac{9}{16}}$$

(5) Alexander simplified the fraction to its simplest form: $$\sin^2 x=\frac{16}{25}$$

(6) Finally, he took the square root of the equality and obtained the desired value of $\sin x$: $$\sin x=\frac45$$

Alexander’s classmates commented on his solution:

a) Eva believed that the error was in step (3). The correct simplification should be: $$\sin^2 x=1-\cot^2 x$$

b) Marek said that step (4) was incorrect. The correct value of $\sin^2 x$ should be: $$\sin^2 x=\frac{1}{1-\frac{9}{16}}$$

c) Martina was convinced that the error was in step (5). The correct simplification should be: $$\sin^2 x=\frac85$$

d) Petra said that step (6) was incorrect. In her opinion, the given task has two solutions, and it holds: $$\sin^2 x=\frac{16}{25}\Leftrightarrow|\sin x|=\frac45\Leftrightarrow\left(\sin x=\frac45 \lor \sin x=-\frac45\right)$$ Determine who was right.