The value of tan6°·tan42°·tan66°·tan78° is:

No two of these angles are complementary (6° + 78° = 84°), so the usual tan k°·tan(90° − k°) = 1 pairing is unavailable. Use instead tanθ·tan(60° − θ)·tan(60° + θ) = tan3θ twice. With θ = 18° it gives tan18°·tan42°·tan78° = tan54°, so tan42°·tan78° = tan54°/tan18°. With θ = 6° it gives tan6°·tan54°·tan66° = tan18°, so tan6°·tan66° = tan18°/tan54°. The two results are reciprocals, so the whole product is 1. Numerical check: $0.10510\times 0.90040\times 2.24604\times 4.70463=1.000$.