exact value for tan(7pi/6 radians)

Answer 1

That would be the same as tan (pi/6). (Tangent is positive inthe third quadrant, where 7pi/6 is located).
pi/6 is 1/3 of a right angle, or 30 degrees. You probably know that the tangent of that angle is 1/sqrt3

Answer 2

tan7pi/6