We then set up the angle [ Angle PSI ] ,
being the sum of [ angle ALPHA ] and [ angle BETA ] .
And because of this , it is necessary for us to place certain restrictions on the size of the 3 angles :
( This is a necessary restriction in order that the { tangent of PSI } may be expressable via a { right-angle triangle } ) .
And as a consequent to these restrictions :
and :
and
Or alternately :
We take note , at this point , that for the [ straight-line F-E-C-B ] passing thru [ Point C ] :
yielding :
We also take note here that the 3 [ angles ] of [ Triangle A-C-B ] always add-up to [ 180 degrees ] , i.e. :
yielding :
Combining the 2 equations above then yields us this relation :
namely that the 2 angles [ Angle TAU ] and [ Angle ALPHA ] are equal-in-value .
And substituting the value of [ L3 ] from above into this equation then yields us this :
Let us now substitute the value for [ L4 ] from above into these 2 equations :
We then have :
And on consolidating terms , we have :
Expressing this in-terms-of [ L1 ] , [ L2 ] , [ L5 ] and [ L6 ] then yields us this equation :
We can then substitute the values for [ L2 ] , [ L5 ] and [ L6 ] from above there-in to arrive at this :
And on consolidating terms , we have :