$\operatorname{cosec} \theta=\frac{2}{\sqrt{3}},$ then $\theta=\ldots \ldots \ldots \ldots$

Prove that,

$\frac{\tan A }{1 \sec A } – \frac{\tan A }{1 \sec A } = 2 \operatorname{cosec} A$

$a \sin \theta=3$ and $a \cos \theta=4,$ then $a=\ldots \ldots \ldots . . .$ (where, $a > 0)$

$\cot \theta=\frac{a}{b},$ then $\frac{\cos \theta-\sin \theta}{\cos \theta+\sin \theta}=\ldots \ldots \ldots$

$\sec \theta=\frac{13}{5},$ then $\cos \theta=\ldots \ldots \ldots \ldots$