Projectiles Help needed

a) A particle is projected with speed 𝑈𝑚𝑠−1
at an acute angle of 𝜃 to the horizontal. Find a
second angle 𝜙 (in terms of 𝜃) to obtain the same range.
b) Suppose that, in addition to the two angles giving equal ranges, the time of flight using 𝜙 is
twice that using 𝜃. What were the two projection angles 𝜃 and 𝜙?
c) What is the ratio of the maximum heights of the two trajectories?

Bit stuck as to how you do this

Work out the range for angle theta.

Assume the range for phi is the same.

Equate and work out a relationship.

So the range is usually U^2 sin2 thetha/g right? Do I replace thetha with phi then equate them together?

Yep.

I got U^2 2sin (phi-thetha). Is this correct?

I have no idea how you ended up with that, but no it's not correct.

Post your working - the main thing you can do is cancel down.

g(U^2 2sin phi)= g(U^2 sin thetha)
I cancelled the g from both sides. Then I made U^2 2sin phi- U^2 2 sin thetha =0

Well "u" and "2" are non-zero so you can cancel them as well ending up with $\sin 2\theta =\sin 2\phi$

At this point you need to have an understanding of the shape of the sine curve.

Do I make it 2sinthetha cos thetha?

There's no need for the double angle formula.

We know that theta and phi are both in the range 0 to 90. So, 2theta and 2phi are in the range 0 to 180.

Have a look at the sine curve in that range. If two values of the angle have the same sine, what's the relationship between the two?

This means both are 0?

I can't imagine why you'd think that.

Here's a plot, with one particular value - the green line. What's the relationship between the two angles (red lines) that take that partiuclar value:

Sorry I get what you're trying to say but I can't quite see the relationship between the two values