To simplify the expression, let's first expand the terms:

(1 - sin α × cos α × tg α) + sin² α + 3
= 1 - sin α cos α tg α + sin² α + 3

Now, we can use trigonometric identities to simplify further. The trigonometric identity we will use is:

sin² α + cos² α = 1

So, we can replace sin² α with (1 - cos² α):

1 - sin α cos α tg α + (1 - cos² α) + 3
= 1 - sin α cos α tg α + 1 - cos² α + 3
= 5 - sin α cos α tg α - cos² α

So, the simplified expression is:

5 - sin α cos α tg α - cos² α