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You can use $Ry$ (y-rotation gate). Its general matrix is $$Ry(\theta) = \begin{pmatrix} \cos(\theta/2) & -\sin(\theta/2) \\ \sin(\theta/2) & \cos(\theta/2) \end{pmatrix}$$ Applying the gate on $|0\rangle$ state, you get a state $$|\psi\rangle = \cos(\theta/2)|0\rangle + \sin(\theta/2)|1\rangle$$ Hence $\cos(\theta/2) = \frac{1}{\sqrt{3}}$ ...