 Hello and welcome to this session. Let us understand the following problem today. Find the value of the expression tan inverse of tan of 3 pi by 4. Now let us write the solution. We know that inverse of tan theta is equal to theta if minus pi by 2 is less than theta is less than pi by 2. The range of the principle value branch of tan inverse is minus pi by 2 to pi by 2 therefore inverse of pi by 4 is equal to tan inverse of is equal to minus tan of pi by 4 which is equal to tan inverse of of minus pi by 4 which is equal to minus pi by 4 therefore the required answer is minus pi by 4 I hope you understood the problem. Bye and have a nice day.