# Tangent identity

Here's a hint for proving that

tan(a) + tan(b) + tan(c) = tan(a) tan(b) tan(c)

if and only if a + b + c is a multiple of π as discussed in this blog post.

Use the identity

tan(α + β) = (tan(α) + tan(β)) / (1 - tan(α) tan(β))

first with α = a + b and β = c. Then apply it again with α = a and β = b. Do some algebra and show that the identity you're trying to prove holds if and only if tan(a+b+c) = 0, i.e. if and only if a + b + c is a multiple of π.