`(sin(90^(@)-theta)sec(180^(@)-theta)sin(-theta))/(sin(180^(@)+theta)cot(360^(@)-theta)"cosec"(90^(@)+theta))`.

Answer

To solve the expression

\[ \frac{\sin(90^\circ - \theta) \cdot \sec(180^\circ - \theta) \cdot \sin(-\theta)}{\sin(180^\circ + \theta) \cdot \cot(360^\circ - \theta) \cdot \csc(90^\circ + \theta)}, \]

we will simplify each trigonometric function step by step.

### Step 1: Simplify \(\sin(90^\circ - \theta)\)
Using the co-function identity:
\[ \sin(90^\circ - \theta) = \cos(\theta). \]

### Step 2: Simplify \(\sec(180^\circ - \theta)\)
In the second quadrant, the secant function is negative:
\[ \sec(180^\circ - \theta) = -\sec(\theta). \]

### Step 3: Simplify \(\sin(-\theta)\)
Using the odd function property of sine:
\[ \sin(-\theta) = -\sin(\theta). \]

### Step 4: Simplify \(\sin(180^\circ + \theta)\)
In the third quadrant, sine is negative:
\[ \sin(180^\circ + \theta) = -\sin(\theta). \]

### Step 5: Simplify \(\cot(360^\circ - \theta)\)
In the fourth quadrant, cotangent is negative:
\[ \cot(360^\circ - \theta) = -\cot(\theta). \]

### Step 6: Simplify \(\csc(90^\circ + \theta)\)
In the second quadrant, cosecant is positive:
\[ \csc(90^\circ + \theta) = \sec(\theta). \]

### Step 7: Substitute all simplified terms back into the expression
Now we can substitute these simplified terms back into the original expression:
\[ \frac{\cos(\theta) \cdot (-\sec(\theta)) \cdot (-\sin(\theta))}{(-\sin(\theta)) \cdot (-\cot(\theta)) \cdot \sec(\theta)}. \]

### Step 8: Simplify the expression
The expression simplifies to:
\[ \frac{\cos(\theta) \cdot \sec(\theta) \cdot \sin(\theta)}{\sin(\theta) \cdot \cot(\theta) \cdot \sec(\theta)}. \]

### Step 9: Cancel common terms
The \(\sec(\theta)\) terms cancel:
\[ \frac{\cos(\theta) \cdot \sin(\theta)}{\sin(\theta) \cdot \cot(\theta)}. \]
The \(\sin(\theta)\) terms also cancel (assuming \(\sin(\theta) \neq 0\)):
\[ \frac{\cos(\theta)}{\cot(\theta)}. \]

### Step 10: Rewrite \(\cot(\theta)\)
Recall that \(\cot(\theta) = \frac{\cos(\theta)}{\sin(\theta)}\):
\[ \frac{\cos(\theta)}{\cot(\theta)} = \frac{\cos(\theta)}{\frac{\cos(\theta)}{\sin(\theta)}} = \sin(\theta). \]

### Final Answer
Thus, the final value of the expression is:
\[ \sin(\theta). \]