The expression tan(θ + π) represents the tangent of an angle that is increased by π radians. In trigonometry, adding π to an angle effectively rotates the angle by 180 degrees, placing it in the opposite direction on the unit circle. Due to the periodic nature of the tangent function, tan(θ + π) is equal to tan(θ). This means that the tangent value remains unchanged when the angle is shifted by π radians, highlighting the symmetry of the tangent function in relation to the unit circle.