  For the XXZ subclass of symmetric two-qubit X states, we study the behavior
of quantum conditional entropy S_{cond} as a function of measurement angle
\theta\in[0,\pi/2]. Numerical calculations show that the function
S_{cond}(\theta) for X states can have at most one local extremum in the open
interval from zero to \pi/2 (unimodality property). If the extremum is a
minimum the quantum discord displays region with variable (state-dependent)
optimal measurement angle \theta^*. Such \theta-regions (phases, fractions) are
very tiny in the space of X state parameters. We also discover the cases when
the conditional entropy has a local maximum inside the interval (0,\pi/2). It
is remarkable that the maxima exist in surprisingly wide regions and the
boundaries for such regions are defined by the same bifurcation conditions as
for those with a minimum. Moreover, the found maxima can exceed the conditional
entropy values at the ends of interval [0,\pi/2] more than by 1%. This instils
hope in the possibility to detect such maxima in experiment.
