To simplify the expression, we can use the trigonometric identities:

cotangent of the sum/difference of angles: cot(x-y) = cotxcoty + 1/sinxsinysine of double angle: sin(2x) = 2sinxcosx

Applying these identities to the given expression:

cot(pi/2-a)*cot(3pi/2+a) + sin(2a)

Since cot(pi/2-a) = -tan(a) and cot(3pi/2+a) = -tan(a), we get:

(-tan(a))(-tan(a)) + sin(2a)
tan(a)tan(a) + sin(2a)
tan^2(a) + 2sin(a)cos(a)

Therefore, the simplified expression is tan^2(a) + 2sin(a)cos(a).