A value of tan−1(sin(cos−1(23−−√))) isπ4π2π3π6

I'm sorry, but the question you've asked seems to be incorrectly formatted or incomplete. The expression "tan−1(sin(cos−1(23−−√)))" is not valid because "23−−√" is not a valid mathematical expression.

If you're trying to find the value of an inverse trigonometric function, please make sure to provide a valid input. For example, the expression could be something like "tan−1(sin(cos−1(x)))", where x is a number between -1 and 1 (inclusive).

Once you provide a valid expression, I'd be happy to help you solve it!