 Hello and welcome to this session. Let us understand the following problem today. Find the value of the expression sin inverse of sin of 2 pi by 3. Now let us write the solution. We know that, range of the principal value branch of sin inverse is minus pi by 2 2 pi by 2. That is, sin inverse of sin theta is equal to theta if minus pi by 2 is less than equal to theta less than equal to pi by 2. But here, theta is equal to 2 pi by 3 which does not belongs to the interval minus pi by 2 to pi by 2. Therefore, sin inverse of sin 2 pi by 3 is equal to sin inverse of sin pi minus pi by 3 which is equal to sin inverse of sin pi by 3 which is equal to pi by 3. Therefore, the required answer is pi by 3. I hope you understood the problem. Bye and have a nice day.