Transform the system of trigonometric equations

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How to extract $\ell$ and $L$ from the following system of equations: $$\alpha=\arctan {R_E \cos \ell \sin L \over R_0 + R_E(1 - \cos \ell \cos L) }$$ $$\beta=\arctan {R_E \sin \ell \cos \alpha \over R_0 + R_E(1 - \cos \ell \cos L) } $$