If cos theta = -5/13 where 180° < theta < 360°, determine, without using a calculator, the value of: 1.1 sin² theta 1.2 tan(360° - theta) 1.3 cos(theta - 135°)

Using reduction formulas: $\cos(180^\circ - x) = -\cos x$ and $\sin(-x) = -\sin x$.

This is the double angle identity for sine: $2 \sin x \cos x = \sin(2x)$.

Using the cofunction identity: $\cos(90^\circ - x) = \sin x$.

This is the double angle identity for cosine: $1 - 2 \sin^2 x = \cos(2x)$.

The simplified expression is $\boxed{\tan(2x)}$.

3. Calculate the value of the expression $(\tan 92^\circ)(\tan 94^\circ)(\tan 96^\circ) \dots (\tan 176^\circ)(\tan 178^\circ)$.

The angles are $92^\circ, 94^\circ, \dots, 178^\circ$. This is an arithmetic progression with a common difference of $2^\circ$.
The number of terms $n$ is found by $178 = 92 + (n-1)2$, which gives $86 = (n-1)2$, so $43 = n-1$, and $n=44$.
Each term can be written using the reduction formula $\tan(90^\circ + \alpha) = -\cot \alpha$:
$\tan 92^\circ = \tan(90^\circ + 2^\circ) = -\cot 2^\circ$
$\tan 94^\circ = \tan(90^\circ + 4^\circ) = -\cot 4^\circ$
...
$\tan 178^\circ = \tan(90^\circ + 88^\circ) = -\cot 88^\circ$

The product is $(-\cot 2^\circ)(-\cot 4^\circ) \dots (-\cot 88^\circ)$.
Since there are 44 terms (an even number), the product of the negative signs is positive.

We can pair terms such that their product is 1: $\cot \alpha \cdot \cot(90^\circ - \alpha) = \cot \alpha \cdot \tan \alpha = 1$.
The terms in the product are $\cot 2^\circ, \cot 4^\circ, \dots, \cot 44^\circ, \cot 46^\circ, \dots, \cot 88^\circ$.
We form pairs:
$(\cot 2^\circ \cdot \cot 88^\circ) = (\cot 2^\circ \cdot \tan 2^\circ) = 1$
$(\cot 4^\circ \cdot \cot 86^\circ) = (\cot 4^\circ \cdot \tan 4^\circ) = 1$
...
The last pair will be $(\cot 44^\circ \cdot \cot 46^\circ) = (\cot 44^\circ \cdot \tan 44^\circ) = 1$.
There are $44/2 = 22$ such pairs.

Since each pair multiplies to 1, the entire product is $1^{22}$.

The value of the expression is $\boxed{1}$.