Find the value of: tan(π/8)

Let x = π/8. Then 2x = π/4.

tan2x = (2tanx) / (1 − tan²x)

tan(π/4) = (2·tan(π/8)) / (1 − tan²(π/8))

Let y = tan(π/8). Then 1 = 2y / (1 − y²)

or y² + 2y − 1 = 0

Therefore y = (−2 ± 2√2) / 2 = −1 ± √2

Since π/8 lies in the first quadrant, y= tan(π/8) is positive.

⇒ tan(π/8) = √2 − 1