As, tan^–1(tan x) = x

Provided x ϵ

Here our x is 2 which does not belong to our range

We know tan(π –θ) = –tan(θ)

∴ tan(θ –π ) = tan(θ)

∴ tan(2–π ) = tan(2)

Now 2–π is in the given range

∴ tan^–1 (tan 2) = 2–π