Multiple Using statements error name does not exist in the current context

Question

I'm trying to set the request headers for the below request, but get an error that the names client and request do not exist in the current context. How do I configure these additional parameters?

public static async Task<string> HttpGetRemoteFileAsync(Uri resourceUri, CancellationToken cancellationToken)
{
    string result = null;

    using (var client = new HttpClient())
    using (request = new HttpRequestMessage(HttpMethod.Get, resourceUri))
    {
        request.Headers.UserAgent.Add(new ProductInfoHeaderValue(new ProductHeaderValue("HeaderValue")));
    }
    using (
        Stream contentStream = await (await client.SendAsync(request, cancellationToken)).Content.ReadAsStreamAsync())
    {
        var content = new HttpRequestStreamReader(contentStream, System.Text.UTF8Encoding.UTF8);
        result = await content.ReadToEndAsync();
    }

    return result;
}