The value of

tan = –1

∴ The question becomes cot^–1(–1)

Let cot^–1(–1) = y

⇒ cot y = –1

= – cot = 1

= cot

= cot

The range of principal value of cot^–1is (0, π)

and cot = –1

∴ The principal value of cot^–1(tan) is .