The number of real solutions of the equation $$\eqalign{ & {\sin ^{ - 1}}\left( {\sum\limits_{i = 1}^\infty {} {x^{i + 1}} - x\sum\limits_{i = 1}^\infty {} {{\left( {{x \over 2}} \right)}^i}} \right) \cr & = {\pi \over 2} - {\cos ^1}\left( {\sum\limits_{i = 1}^\infty {} {{\left( {{{ - x} \over 2}} \right)}^i} - \sum\limits_{i = 1}^\infty {} {{\left( { - x} \right)}^i}} \right) \cr} $$ lying in the interval $$\left( { - {1 \over 2},{1 \over 2}} \right)$$ is ........... .

(Here, the inverse trigonometric functions sin^$$-$$1 x and cos^$$-$$1 x assume values in $${\left[ { - {\pi \over 2},{\pi \over 2}} \right]}$$ and $${\left[ {0,\pi } \right]}$$, respectively.)

Let f : [0, 4$$\pi$$] $$\to$$ [0, $$\pi$$] be defined by f(x) = cos^$$-$$1 (cos x). The number of points x $$\in$$ [0, 4$$\pi$$] satisfying the equation $$f(x) = {{10 - x} \over {10}}$$ is