Stuck Flathead Valve on Toilet Supply Line

Hi lads and lassies,

I'm in the middle of a DIY bathroom job and need some help. I'm trying to replace my broken toilet siphon, but I'm completely stuck at the first hurdle - shutting off the water supply. The culprit? A stubborn flathead valve on the supply line that refuses to budge.

I've been wrestling with this valve, but it's like it's glued shut. I've tried all my usual tricks:

• Muscle power: Pushing and turning with all my might, but it won't give.
• Screwdriver: Using the right size flathead, but it's starting to strip the head.
• WD-40: Drenched the valve in lubricant, but still no movement.

• Any ideas on how to coax this stubborn valve open? Are there special tools or techniques I'm missing?
• Should I try heating it up slightly (carefully, of course)?
• Should I just cut my losses and call a plumber (gulp)?

Any advice, wisdom, or shared misery would be greatly appreciated!

Thanks in advance!