tan(α+β)
= sin(α+β)/cos(α+β)
= ( sinα cosβ + cosα sinβ )/(cosαcosβ - sinαsinβ)
= ((sinα cosβ + cosα sinβ)/(cosαcosβ))/(1 - (sinαsinβ)/(cosαcosβ))
= ( sinα/cosα + sinβ/cosβ )/(1 - (sinα/cosα)(sinβ/cosβ))
= ( tanα + tanβ )/(1 - tanα tanβ )
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