If $\theta$ is an acute angle and $\sin 10\theta =\cos \left(5\theta -15°\right)$, then find the value of $\theta$ in degree $\left(°\right)$.

Prove that,

$\frac{\cos \theta }{\sec \left(90-\theta \right)+1}+\frac{\sin \left(90-\theta \right)}{\mathrm{cosec}\theta -1}=2\cot \left(90-\theta \right)$

Find the value of ${\sin }^{2}15°+{\sin }^{2}75°$

$\frac{\cos 80°}{\sin 10°}+\cos 59°\mathrm{cosec} 31°=$ _____

Prove that $\tan 10°\tan 25°\tan 45°\tan 65°\tan 80°=1$