We need to find the value of

Let 2 cot^-1 3 = y

Then,

Substituting 2 cot^-1 3 = y,

Using the trigonometric identity,

So,

We know that,

…(i)

We know that, by trigonometric identity,

Take reciprocal of both sides,

Put y = y/2.

Putting the value of cot y in equation (i),

Put the value of derived above and also .

=7