Testing Hypothesis

Please help my to solve this question:

let X is a random variable with density f(x,θ) given by
f(x,θ)= 1+Θ2(0.5-x) if 0<x<1 ,-1≤Θ≤1
and 0 ,otherwise .
consider testing H0:θ=0 vs. H1:θ≠0.
a) show that the test that reject H0 if X≤α is an unbiased test of size α.
b) find the LRT of size α=0.05 .
note:

Θ2 : represent the square value of Θ
0:zero.
Thank you