Learn English – “Though”, “even though” and “although”

These two are not equivalent. Even though is used to introduce a condition which currently is true, while even if introduces a hypothetical condition that is not yet true.

I'm going to the park even though it's raining.

This means that it's raining right now, but I'm going to the park anyway.

I'm going to the park even if it's raining.

This means that it's not yet raining, but I will go to the park even if it starts to rain. Note that in this case the present progressive I'm going actually indicates a near future action.

Though can definitely be used at the beginning of a sentence, and has a long history of doing so. Consider Isaiah 1:18 from the King James Bible:

Though your sins be as scarlet, they shall be as white as snow; though they be red like crimson, they shall be as wool.

TheFreeDictionary.com cites this usage rule:

Although and though are interchangeable as conjunctions, but to start a clause, use although.

However, this seems overly fussy and prescriptive. Consider the following:

I went ahead and chopped all the wood, though no one told me to.

You left without your luggage, though I can't imagine why.

Those sound to me like perfectly fine English. They would be perfectly fine using although as well. That, to me, feels like interchangeability, pure and simple. In fact, I can think of no examples in which though cannot be used interchangeably with although. Though your mileage may vary.