To simplify this expression, we first need to rewrite the trigonometric functions in terms of their basic trigonometric identities.

Recall that:

Now, let's substitute these identities into the expression:

cos(π - β) - 3sin(-3π/2) / cos(β - 3π)

= cos(π - β) - 3(-sin(3π/2)) / cos(β - 3π)

= cos(π - β) + 3sin(3π/2) / cos(β - 3π)

= -cos(β) + 3(-1) / -cos(β)

= -cos(β) - 3 / -cos(β)

= 3 + cos(β) / cos(β)

Therefore, the simplified expression is 3 + 1 / cos(β) = 4 / cos(β)