Explain how the electron pair repulsion theory can be used to deduce the shape of, and the bond angle in, PF3

Phosphorous has five electrons in its outermost shell of electrons. Fluorine provides three electrons to the phosphorous allowing the formation of a stable central phosphorous atom which now has 8 electrons and 3 fluorine atoms which now also share 8 electrons in its outershell. However as there are only 3 bonding pairs there must be a lone pair of electrons in this molecule. As bond pairs repel each other you would expect a tetrahedral shape to the molecule with a bond angle of 109 however due to the presence of the lone pair, there is more repulsion which distorts the shape slightly and it becomes trigonal pyramidal with a bond angle of 107.