Answer: see proof below
<u>Step-by-step explanation:</u>
Use the following Sum Identity:

Given: A + B + C = 180° → A + B + C = π
<u>Proof LHS → RHS</u>
Given: A + B + C = π
Multiply by 2: 2(A + B + C = π)
→ 2A + 2B + 2C = 2π
→ 2A + 2B = 2π - 2C
Apply tan: tan(2A + 2B = 2π - 2C)
→ tan (2A + 2B) = tan(2π - 2C)
→ tan (2A + 2B) = - tan 2C
Simplify: tan 2A + tan 2B = -tan 2C (1 - tan 2A · tan 2B)
Distribute: tan 2A + tan 2B = -tan 2C + tan 2A · tan 2B · tan 2C
Add tan 2C: tan 2A + tan 2B + tan 2C = tan 2A · tan 2B · tan 2C
LHS = RHS is proven