Sina/sitt Is a construct I have only seen in the Nordic languages. It is a reflexive pronoun that reflects back the third person (sing or plur) , just as Zmrzlina points out below. What does this mean then? I'll give you an example:
Han tvättar sina kläder - His is washing his clothes (his own ones) Han tvättar hans kläder - He is washing his clothes (someone else's)
We don't have this in 1st or 2nd person.
Thank you! I feel all of my explanations in this thread are a bit rambling …
You're correct, it is obligatory to use the reflexive possessives for the third person in Swedish. If you say Han hittade sin bok, he found his own book, but as soon as you say Han hittade hans bok, the book he found cannot be his own, it has to belong to some other male.
This system is a bit weak in some places and you can definitely hear native speakers make mistakes, but it's still safe to talk about right and wrong here, although it may well be that the system will look different in fifty years time.
At least my teachers used to tell me that it isn't wrong to say я взял мое [whatever], it's just that it puts a certain special stress on the whatever being 'mine'. Which means that using свой in that case is not obligatory. While with her or him it's obligatory or meaning changes into the thing belonging to someone else. Например можно сказать Я нашел мою книгу, а не твою.
For some reason I can't reply to Arnauti's post below (no Reply link), so replying here: You're correct, and your explanation is very good (although I would put your example after the first sentence since it illustrates what you said in the beginning). Now back to Swedish: is it obligatory to use reflexive possessives in Swedish?
It is quite probably related to the other "reflexive particle" (sig - not sure if you would classify this as a pronoun) which also exists in German (sich - his/her/it/them-self) and behaves the same way in that the only other forms are myself (mich) and yourself (dich).