atan(α) + atan(β) | = atan( (α + β) / (1 - αβ) ) |

atan(y_{α}/x_{α}) + atan(y_{β}/x_{β}) | = |

θ_{α} + θ_{β} | = |

= θ_{?} | |

= atan(y_{?}/x_{?}) |

(x_{?},y_{?}) = | (x_{α},y_{α}) + y_{β} (x_{α},y_{α})^{⟂} / ‖x_{α}y_{α}‖ |

= | (x_{α},y_{α}) + y_{β} (-y_{α},x_{α}) / ‖x_{α}y_{α}‖ |

= | (1,y_{α}) + y_{β} (-y_{α},1) / x_{β} |

y_{?} = | y_{α} + y_{β}/x_{β} = α + β |

x_{?} = | 1 - y_{β}y_{α}/x_{β} = 1 + α β |