Question: parameterize equation

Can someone help me with this?? i have x^2+y^2+z^2=1 and y=z and now i find the equation of their intersection which is x^2+2z^2=1 but then i have problem parameterize it since i let x=cost, y=sint, and since y=z, then z=sint but if i plug it back to the equation (cost)^2+2(sint)^2=1, which is not correct, can someone help me wut to set for z?? Thx
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