Write the value of tan(2tan⁻¹(1/5))

tan[2tan⁻¹(1/5)]
We know that 2tan⁻¹x = tan⁻¹(2x/(1-x²))
Here, x = 1/5
= tan⁻¹(2 × (1/5) / (1 - (1/5)²))
= tan⁻¹(2/5 / (1 - 1/25))
= tan⁻¹(2/5 / (24/25))
= tan⁻¹(2/5 × 25/24)
= tan⁻¹(5/12)
= 5/12