Calculate, without the use of a calculator: \[ \frac{\sin \left(180^{\circ}+x\right) \tan \left(360^{\circ}+x\right) \cos \left(180^{\circ}-x\right) \sec 300^{\circ}}{\sec ^{2} x-\tan ^{2} x} \]

Question

(a) Calculate, without the use of a calculator:
\[
\frac{\sin \left(180^{\circ}+x\right) \tan \left(360^{\circ}+x\right) \cos \left(180^{\circ}-x\right) \sec 300^{\circ}}{\sec ^{2} x-\tan ^{2} x}
\]

(b) If \(\sin 2 x=0,432\) for \(x \in\left[0^{\circ} 180^{\circ}\right]\), determine the value(s) of \(x\).