$\theta ={tan}^{-1}\left(\frac{{\mathrm{v\text{'}}}_x}{{\mathrm{v\text{'}}}_y}\right)={tan}^{-1}\left(\frac{-cos\left(\alpha \right)sin\left(\gamma \right)-sin\left(\alpha \right)sin\left(\beta \right)cos\left(\gamma \right)}{-sin\left(\alpha \right)sin\left(\gamma \right)+cos\left(\alpha \right)sin\left(\beta \right)cos\left(\gamma \right)}\right)$