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Probably the main problem is the bad definition of $Ry$ gate in your excercise. However, I will try to give you another way how to solve the problem without many matrix calculations. Lets assume that we have a qubit in state $|0\rangle$. If we apply $Ry(\theta)$ gate we get the qubit in state $$\cos(\theta/2)|0\rangle + \sin(\theta/2)|1\rangle.$$ This is ...
I think $R_y(\theta)$is possibly wrongly defined. If we define it as usual, we write $$R_y(\theta)=\exp\left(-i\frac\theta2 Y\right)=\begin{pmatrix} \cos(\theta/2) & -\sin(\theta/2) \\ \sin(\theta/2) & \cos(\theta/2) \end{pmatrix}\neq \begin{pmatrix} \cos(\theta/2) & \sin(\theta/2) \\ -\sin(\theta/2) & \cos(\theta/2) \end{pmatrix}$$ The ...