For $0 < x < 2 \pi$, what is the sum of all values of $x$ that simultaneously satisfy the equation $4 \cos ^ { 2 } x - 1 = 0$ and the inequality $\sin x \cos x < 0$? [3 points]
(1) $\frac { 10 } { 3 } \pi$
(2) $3 \pi$
(3) $\frac { 8 } { 3 } \pi$
(4) $\frac { 7 } { 3 } \pi$
(5) $2 \pi$

For the function $f(x) = \sin\frac{\pi}{4}x$, find the sum of all natural numbers $x$ satisfying the inequality $$f(2+x)f(2-x) < \frac{1}{4}$$ for $0 < x < 16$. [3 points]

The set of all possible values of $\theta$ in the interval $( 0 , \pi )$ for which the points $( 1,2 )$ and $( \sin \theta , \cos \theta )$ lie on the same side of the line $x + y = 1$ is?
(1) $\left( 0 , \frac { \pi } { 2 } \right)$
(2) $\left( \frac { \pi } { 4 } , \frac { 3 \pi } { 4 } \right)$
(3) $\left( 0 , \frac { 3 \pi } { 4 } \right)$
(4) $\left( 0 , \frac { \pi } { 4 } \right)$

All possible values of $\theta \in [ 0,2 \pi ]$ for which $\sin 2 \theta + \tan 2 \theta > 0$ lie in :
(1) $\left( 0 , \frac { \pi } { 2 } \right) \cup \left( \pi , \frac { 3 \pi } { 2 } \right)$
(2) $\left( 0 , \frac { \pi } { 2 } \right) \cup \left( \frac { \pi } { 2 } , \frac { 3 \pi } { 4 } \right) \cup \left( \pi , \frac { 7 \pi } { 6 } \right)$
(3) $\left( 0 , \frac { \pi } { 4 } \right) \cup \left( \frac { \pi } { 2 } , \frac { 3 \pi } { 4 } \right) \cup \left( \pi , \frac { 5 \pi } { 4 } \right) \cup \left( \frac { 3 \pi } { 2 } , \frac { 7 \pi } { 4 } \right)$
(4) $\left( 0 , \frac { \pi } { 4 } \right) \cup \left( \frac { \pi } { 2 } , \frac { 3 \pi } { 4 } \right) \cup \left( \frac { 3 \pi } { 2 } , \frac { 11 \pi } { 6 } \right)$